ChemWiki - User contributions [en]

OliviaPiniInorganicLab

2018-05-18T15:11:28Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine''

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a delocalised sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap of similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy totally bonding delocalised π orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally delocalized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases and represents one of the degenerate HOMO orbitals These orbitals are formed by the two sets of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. This is overall a delocalised π-bonding orbital, however it does have some anti-bonding character as there is a node going down in between the two clouds of electron density and this is a significant node as it is not due to a node within an atomic orbital. The two bonding overlaps are antibonding with respect to eachother, however as this interaction occurs over a larger distance it is weaker then the bonding interaction and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogens.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO13 in benzene and MO16 in borazine and so the orbital in borazine is higher in energy, however they share the same bonding and anti-bonding characteristics. In both cases the orbital is overall non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene as nitrogen is more electronegative then carbon. The 1s orbitals on the hydrogen's attached to the boron's are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directly bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. This equal distribution of charge supports the idea of having a symmetric molecule with complete even delocalisation of electron density all over the molecule. The hydrogen's have a positive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density towards themselves. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the boron's as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. The boron's in borazine have a positive charge distribution as they are less electronegative then nitrogen so do not attract electron density towards themselves as well. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons and hydrogen's, whereas borazine has a less symmetric distribution due to differences in electronegativity between nitrogen and boron. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogen's and boron's in borazine, which is expected as carbons electronegativity is intermittent of that of boron and nitrogen (it is more electronegative then boron but less electronegative then nitrogen).

===Concept of aromaticity===

There are many ways to categorize if a molecule is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the molecule will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are (3):

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induced pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reactions in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be regained.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However, many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) p-electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine (Fig. 17) there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electrons that will help add to the aromatic character of the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty (Fig. 18). Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation and aromaticity - s-orbitals and the p-orbitals in the plane of the ring can also take part in delocalised bonding adding to the overall aromaticity of the molecule. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals overlapping causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping in a sigma fashion, causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

3) M. Palusiak, T. M. Krygowski, ''Chem. Eur. J''. 2007, 13, 7996 – 8006.

OliviaPiniInorganicLab

2018-05-18T15:06:20Z

Op116: /* References */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine''

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a delocalised sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap of similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy totally bonding delocalised π orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally delocalized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases and represents one of the degenerate HOMO orbitals These orbitals are formed by the two sets of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. This is overall a delocalised π-bonding orbital, however it does have some anti-bonding character as there is a node going down in between the two clouds of electron density and this is a significant node as it is not due to a node within an atomic orbital. The two bonding overlaps are antibonding with respect to eachother, however as this interaction occurs over a larger distance it is weaker then the bonding interaction and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogens.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO13 in benzene and MO16 in borazine and so the orbital in borazine is higher in energy, however they share the same bonding and anti-bonding characteristics. In both cases the orbital is overall non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene as nitrogen is more electronegative then carbon. The 1s orbitals on the hydrogen's attached to the boron's are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directly bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. This equal distribution of charge supports the idea of having a symmetric molecule with complete even delocalisation of electron density all over the molecule. The hydrogen's have a positive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density towards themselves. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the boron's as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. The boron's in borazine have a positive charge distribution as they are less electronegative then nitrogen so do not attract electron density towards themselves as well. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons and hydrogen's, whereas borazine has a less symmetric distribution due to differences in electronegativity between nitrogen and boron. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogen's and boron's in borazine, which is expected as carbons electronegativity is intermittent of that of boron and nitrogen (it is more electronegative then boron but less electronegative then nitrogen).

===Concept of aromaticity===

There are many ways to categorize if a molecule is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the molecule will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

3) M. Palusiak, T. M. Krygowski, ''Chem. Eur. J''. 2007, 13, 7996 – 8006.

OliviaPiniInorganicLab

2018-05-18T15:04:30Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine''

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a delocalised sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap of similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy totally bonding delocalised π orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally delocalized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases and represents one of the degenerate HOMO orbitals These orbitals are formed by the two sets of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. This is overall a delocalised π-bonding orbital, however it does have some anti-bonding character as there is a node going down in between the two clouds of electron density and this is a significant node as it is not due to a node within an atomic orbital. The two bonding overlaps are antibonding with respect to eachother, however as this interaction occurs over a larger distance it is weaker then the bonding interaction and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogens.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO13 in benzene and MO16 in borazine and so the orbital in borazine is higher in energy, however they share the same bonding and anti-bonding characteristics. In both cases the orbital is overall non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene as nitrogen is more electronegative then carbon. The 1s orbitals on the hydrogen's attached to the boron's are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directly bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. This equal distribution of charge supports the idea of having a symmetric molecule with complete even delocalisation of electron density all over the molecule. The hydrogen's have a positive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density towards themselves. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the boron's as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. The boron's in borazine have a positive charge distribution as they are less electronegative then nitrogen so do not attract electron density towards themselves as well. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons and hydrogen's, whereas borazine has a less symmetric distribution due to differences in electronegativity between nitrogen and boron. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogen's and boron's in borazine, which is expected as carbons electronegativity is intermittent of that of boron and nitrogen (it is more electronegative then boron but less electronegative then nitrogen).

===Concept of aromaticity===

There are many ways to categorize if a molecule is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the molecule will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T15:02:27Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine''

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a delocalised sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap of similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy totally bonding delocalised π orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally delocalized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases and represents one of the degenerate HOMO orbitals These orbitals are formed by the two sets of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. This is overall a delocalised π-bonding orbital, however it does have some anti-bonding character as there is a node going down in between the two clouds of electron density and this is a significant node as it is not due to a node within an atomic orbital. The two bonding overlaps are antibonding with respect to eachother, however as this interaction occurs over a larger distance it is weaker then the bonding interaction and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogens.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO13 in benzene and MO16 in borazine and so the orbital in borazine is higher in energy, however they share the same bonding and anti-bonding characteristics. In both cases the orbital is overall non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene as nitrogen is more electronegative then carbon. The 1s orbitals on the hydrogen's attached to the boron's are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directly bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. This equal distribution of charge supports the idea of having a symmetric molecule with complete even delocalisation of electron density all over the molecule. The hydrogen's have a positive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density towards themselves. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the boron's as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. The boron's in borazine have a positive charge distribution as they are less electronegative then nitrogen so do not attract electron density towards themselves as well. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons and hydrogen's, whereas borazine has a less symmetric distribution due to differences in electronegativity between nitrogen and boron. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogen's and boron's in borazine, which is expected as carbons electronegativity is intermittent of that of boron and nitrogen (it is more electronegative then boron but less electronegative then nitrogen).

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:55:50Z

Op116: /* MO Comparisons */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine''

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a delocalised sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap of similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy totally bonding delocalised π orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally delocalized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases and represents one of the degenerate HOMO orbitals These orbitals are formed by the two sets of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. This is overall a delocalised π-bonding orbital, however it does have some anti-bonding character as there is a node going down in between the two clouds of electron density and this is a significant node as it is not due to a node within an atomic orbital. The two bonding overlaps are antibonding with respect to eachother, however as this interaction occurs over a larger distance it is weaker then the bonding interaction and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogens.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO13 in benzene and MO16 in borazine and so the orbital in borazine is higher in energy, however they share the same bonding and anti-bonding characteristics. In both cases the orbital is overall non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene as nitrogen is more electronegative then carbon. The 1s orbitals on the hydrogen's attached to the boron's are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directly bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:46:08Z

Op116: /* Borazine */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine''

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:45:33Z

Op116: /* Benzene */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:45:15Z

Op116: /* Benzene */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene''

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene''

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:44:39Z

Op116: /* BBr3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3''

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:43:31Z

Op116: /* BBr3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace: {{DOI|10042/202423}}

Frequency file from Gaussian: [[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:43:12Z

Op116: /* BBr3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3''

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:41:37Z

Op116: /* Energy */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = [E(NH3)+E(BH3)] - E(NH3BH3)= [(-56.55777) + (-26.61532)] - (-83.22469)= 0.0518 a.u. = 136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. The difference can be attributed to this molecule having poorer orbital overlap as boron is less electronegtative then nitrogen so will have higher energy orbitals. Whereas in ethane, the two carbon atoms will have the exact same energy orbitals and so will have a larger energy splitting and so stabilization.(2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:37:02Z

Op116: /* NH3BH3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:36:15Z

Op116: /* NH3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:34:30Z

Op116: /* Optimising a Molecule of BH3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = IR strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations, however from Table 3 it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the symmetric stretch that would appear at 2579.74cm-1 is IR inactive as it does not result in a change in dipole of the molecule. This means it will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen from Fig. 4 overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the computed antibonding orbitals the nodal planes are more pronounced, with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:24:03Z

Op116: /* Optimising a Molecule of BH3 */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:22:52Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

''Fig. 17 = s-orbitals in overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

''Fig. 18 = p-orbitals in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine''

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

File:OliviaPiniBorazine MO16.png

2018-05-18T14:22:00Z

Op116:

OliviaPiniInorganicLab

2018-05-18T14:21:37Z

Op116: /* MO Comparisons */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazine_MO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

Fig. 17 = p-orbitals in in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

File:OliviaPiniBorazine MO7.png

2018-05-18T14:21:12Z

Op116:

File:OliviaPiniBorazineMO16.png

2018-05-18T14:20:46Z

Op116: Op116 uploaded a new version of File:OliviaPiniBorazineMO16.png

OliviaPiniInorganicLab

2018-05-18T14:20:28Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazine_MO7.png]]

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

Fig. 17 = p-orbitals in in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

File:OliviaPiniBorazineMO16.png

2018-05-18T14:20:01Z

Op116: Op116 uploaded a new version of File:OliviaPiniBorazineMO16.png

File:OliviaPiniBenzene MO7.png

2018-05-18T14:18:06Z

Op116:

OliviaPiniInorganicLab

2018-05-18T14:17:39Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

[[File:OliviaPiniBenzene_MO7.png]] [[File:OliviaPiniBorazineMO15.png]]

[[File:OliviaPiniBenzeneMO14.png]] [[File:OliviaPiniBorazineMO15.png]]

Fig. 17 = p-orbitals in in the plane of the ring overlapping and causing delocalisation so adding to aromaticity. a) Benzene b) Borazine

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T14:13:26Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The overlapping of pz-orbitals is not a good description for aromaticity as other orbitals also take part in bonding that leads to delocalisation. For example in the first valence MO of both benzene and borazine there is overlap of a 2s-orbitals on all the atoms, forming a delocalised cloud of electron that will help add to the aromatic character to the molecules. Additionally, the p-orbitals in the plane of the ring can also overlap in a sigma fashion (head-on overlap) and again form a delocalised cloud of electron density, creating aromaticty. Therefore, overall it is not just the p-orbitals orthogonal to the plane of the ring that can overlap causing delocalisation - s-orbitals and the p-orbitals in the plane of the ring can also do similar reactions adding to the aromaticity. This is known as σ-aromaticty and demonstrates why just using overlapping pz-orbitals is not a perfect representation of the bonding in the molecule.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T13:56:05Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuously bonded p-orbitals orthogonal to the plane of the ring, forming electron clouds above and below the plane of the ring, showing delocalisation. However,many other MOs were computed with sigma character that would also have played a part in the overall bonding of the molecule and so it can be seen that aromaticity is much more complex then just a cyclic array of continuously conjugated p-orbitals perpendicular to the plane of the ring with (4n + 2) electrons.

The

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

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T13:36:41Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the orbitals representing pi-bonds illustrated continuous electron clouds above and below the plane of the ring, showing delocalisation.

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

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T13:02:11Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

One of the common basic ideas of aromaticity is that there is delocalisation of electron density over the whole molecule. The real MOs represent this very effectively as all the pi-orbitals

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

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T12:49:23Z

Op116: /* Concept of aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons then using this theory, it is named anti-aromatic and should display particular destabilization and instability. Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

Other ground state properties have also been discovered to indicate if a molecule is aromatic or not and these are:

*Aromatic compounds will be more stable then if they were to have localized single and double bonds and this difference in energy is referred to as resonance energy.

*The bond lengths will be in between those expected for the typical single and double bonds of that system, illustrating the delocalisation of the electrons all over the molecule.

*Placing these systems in an external magnetic field causes a pi-electron ring current, causing the hydrogen's outside the ring to have a higher chemical shift value. The hydrogen's in exocyclic environments feel both the external magnetic field as well as the induce pi current, meaning they are more deshielded.

*Aromatic molecules normally take part in reaction in which the pi-electron structure is reformed (e.g. aromatic substitution), as it allows the extra stabilization of these systems to be reformed.

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

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T12:29:55Z

Op116: /* Aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

===Concept of aromaticity===

There are many ways to categorize if a molecule is is aromatic or not. One of these ways is using Huckel's Rule, which states that a planar compound with a contiguous, cyclic array of p-orbitals perpendicular to the plane of the ring will be aromatic if it has (4n + 2) p-electrons. These aromatic compounds will also display an increased level of stabilization. If a molecule has all these characteristics but only (4n) p-electrons Both benzene and borazine are planar with interacting p-orbitals on all the atoms and have 6 p-electrons (4n +2 = 6 when n=1), meaning using Huckel's rule they are both aromatic.

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

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T12:12:27Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral. Overall, benzene has a symmetric charge distribution, due to it being made of only carbons, whereas borazine has a less symmetric distribution to differences in electronegativity. Additionally, the charge distribution of the carbons in benzene is in between that of the nitrogens and borons in borazine, which is expected as carbons electronegativity is intermittent of that of borazine and nitrogen (it is more electronegative then boron but less electronegative then nitrogen.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T12:07:06Z

Op116: /* Aromaticity */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The hydrogens have a postive charge distribution compared to the carbons as they are less electronegative and so will attract less electron density. Whereas in borazine, the nitrogen's have a much more negative charge density, both then the borons as well the carbons in benzene, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more positive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-18T12:02:20Z

Op116:

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the carbons have the same electronegativity, meaning the charge is shared equally over all the atoms. The equal distribution of charge supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. Whereas, in borazine the nitrogens have a postive charge distribution compared to the carbons in benzene as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-17T16:42:28Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and all of the hydrogen's. Also overall it is much more neutral then borazine as it is made only of carbons and so all the electronegatives are the same, meaning the charge is shared equally over all the atoms, explaining why overall it is more neutral. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-17T16:31:53Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

OliviaPiniInorganicLab

2018-05-17T16:27:42Z

Op116:

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

''Fig. 1 = Summary Table of BH3''

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 1 = Item Table of BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

''Table 2 = Low frequencies of BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

''Fig. 2 = JMol of BH3''

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

''Table 3 = Ir strechtes of BH3''

[[File:IRBH3SPECTRUM.png|400px]]

''Fig. 3 = IR spectrum of BH3''

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

''Fig. 4 = MO Diagram of BH3 (1)''

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

''Fig. 5 = Summary Table 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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

''Table 4 = Item Table of NH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

''Table 5 = Low frequencies of NH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 6 = JMol of NH3''

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

''Figure 7 = Summary Table of NH3BH3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 6 = Item Table of NH3BH3''

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

''Table 7 = Low frequencies of NH3BH3''

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 8 = JMol of NH3BH3''

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol. (2)

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

''Figure 9 = Summary Table of BBr3''

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

''Table 8 = Item Table of BBr3'

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

''Table 9 = Low frequencies of BBr3'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 10 = JMol of BBr3'

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

''Figure 11 = Summary Table of benzene'

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

''Table 10 = Item Table of benzene'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

''Table 11 = Low frequencies of benzene'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 12 = JMol of benzene'

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

''Figure 13 = Summary Table of borazine'

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

''Table 12 = Item table of borazine'

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

''Table 13 = Low frequencies of borazine'

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

''Figure 14 = JMol of borazine'

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|-
|[[File:OliviaPiniBenzeneMO13.png]]
|[[File:OliviaPiniBorazineMO16.png]]
|This is MO20 in benzene and MO16 in borazine and so the orbital in benzene is higher in energy, however they are share the same bonding and anti-bonding characteristics. In both cases the orbital is non-bonding with the orbitals being present most probably being 1s orbitals on the hydrogen's. This is easily seen in the benzene orbital as the carbons are actually pointing out of the orbital and so the orbital is not centered on them but polarized towards them as carbon is more electronegative then hydrogen. In the case or borazine the orbitals are again 1s orbitals on the hydrogen with the green areas on the nitrogen and boron atoms being an artifact of the calculation. In this case the 1s orbitals on the hydrogen's attached to the nitrogen are much less diffused and much more polarised towards to the nitrogen then in benzene and nitrogen is more electronegative. The 1s orbitals on the hydrogens attached to the borons are hardly polarized towards the boron atom as hydrogen is more electronegative compared to boron. Although these atoms are of opposite phases they are not directed bonding and so overall the molecule would be non-bonding.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table 14: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table 15: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure 15: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure 16: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

==References==

1) Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 2018).

2)Chemistry 301, https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html, (accessed May 2018).

File:OliviaPiniBorazineMO16.png

2018-05-17T16:11:49Z

Op116:

File:OliviaPiniBenzeneMO13.png

2018-05-17T16:11:20Z

Op116:

OliviaPiniInorganicLab

2018-05-17T16:10:28Z

Op116:

OliviaPiniInorganicLab

2018-05-17T15:43:20Z

Op116:

OliviaPiniInorganicLab

2018-05-17T15:32:59Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

[[File:IRBH3SPECTRUM.png|400px]]

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

'''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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol.

REFERENCE: https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table x: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table x: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure x: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|370px]]

''Figure x: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

OliviaPiniInorganicLab

2018-05-17T15:32:50Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

[[File:IRBH3SPECTRUM.png|400px]]

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

'''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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol.

REFERENCE: https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table x: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table x: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure x: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|350px]]

''Figure x: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

OliviaPiniInorganicLab

2018-05-17T15:32:37Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

[[File:IRBH3SPECTRUM.png|400px]]

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

'''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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol.

REFERENCE: https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table x: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table x: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure x: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png|400px]]

''Figure x: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

OliviaPiniInorganicLab

2018-05-17T15:32:26Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

[[File:IRBH3SPECTRUM.png|400px]]

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

'''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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol.

REFERENCE: https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table x: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table x: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure x: Charge Distribution using colour in benzene.''

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

''Figure x: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

OliviaPiniInorganicLab

2018-05-17T15:32:07Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

[[File:IRBH3SPECTRUM.png|400px]]

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

'''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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol.

REFERENCE: https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|}

===Charge Distribution analysis===

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table x: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table x: Charge Distribution in borazine.''

[[File:OliviaPiniColouredChargeBenzene.png]]

''Figure x: Charge Distribution using colour in benzene.''

[[File:OliviaPiniColouredChargeBorazine.png]]

''Figure x: Charge Distribution using colour in borazine.''

From both of the above methods of depicting charge it can be seen that in benzene the charge is the same for all the carbons and so all of the hydrogen's. This supports the idea of having a symmetric molecule with complete delocalisation of electron density evenly all over the molecule. The nitrogens have a postive charge distribution compared to the carbons as they are less electronegative. Whereas in borazine, the nitrogen's have a much more negative charge density then the borons, as they are more electronegative and so pull the electrons in both the sigma and pi bonds towards themselves. Like in benzene, the hydrogen's attached to the nitrogen have a more postive charge density, as they are more electropositive. Whereas, the hydrogen's attached to the boron are basically neutral. This is because hydrogen is more electronegative then boron and so should have a more negative charge distribution but hydrogen's don't want to hold so much electron density and so appear almost neutral.

File:OliviaPiniColouredChargeBorazine.png

2018-05-17T15:19:09Z

Op116:

File:OliviaPiniColouredChargeBenzene.png

2018-05-17T15:18:51Z

Op116:

OliviaPiniInorganicLab

2018-05-17T15:18:33Z

Op116:

OliviaPiniInorganicLab

2018-05-17T15:15:57Z

Op116: /* Charge Distribution analysis */

==Optimising a Molecule of BH3==

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_BH3_summary_table.png]]

'''Item Table ''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000192 0.000450 YES
RMS Force 0.000126 0.000300 YES
Maximum Displacement 0.000763 0.001800 YES
RMS Displacement 0.000500 0.001200 YES
Predicted change in Energy=-2.202660D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BH3_FREQ_wiki.log| OLIVIAPINI_BH3_FREQ_wiki.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.2260 -0.1036 -0.0056 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6742
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BH3_FREQ_wiki.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Vibrations''' :

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163.72
|92.4740
|A2''
|Yes
|Out-of-plane bend
|-
|1213.67
|14.0890
|E'
|Very Slight
|Bend
|-
|1213.67
|14.0926
|E'
|Very Slight
|Bend
|-
|2579.74
|0.0000
|A1'
|No
|Symmetric Stretch
|-
|2712.67
|126.4185
|E'
|Yes
|Asymmetric Stretch
|-
|2712.67
|126.4089
|E'
|Yes
|Asymmetric Stretch
|}

[[File:IRBH3SPECTRUM.png|400px]]

This IR spectrum shows only 3 peaks, illustrating only 3 vibrations. whereas from the above table it can be seen that in fact BH3 has 6 vibrations. The reason only 3 are seen is firstly because the asymmetric stretch at 2579.74cm-1 is not IR active as it does not result in a change in dipole of the molecule and so will not absorb IR radiation and so doesn't give a peak. Also there are two peaks at both 1213.67 and 2712.67 cm-1 illustrating degenerate bends and asymmetric stretches respectively. Consequently only 1 peak will be seen in each case in the IR spectrum in stead of 2. This explains why three peaks are seen in the spectrum instead of the expected 6.

'''MO Diagram''' :

[[File:IBH3MODIAGRAM.png|600px]]

As can be seen overall the qualitative MO theory predictions mainly match those computed by Gaussian and so it can be said that it is a useful and accurate qualitative procedure. All the computed orbitals appear in the same positions as those predicted by MO theory, however the unoccupied computed orbitals are more diffused then those occupied ones and that is not shown in the qualitative MO diagram. Additionally, for the anti bonding orbitals the nodal planes are more pronounced with the orbitals actually beginning to point away from each other due to repulsion, as seen especially in the top two orbitals and this is not depicted in the qualitative approach. However, overall the two are a good match with all orbitals being in the same positions and with the same phases and so confidence can be had in the qualitative MO theory and predictions.

==Association energies: Ammonia-Borane==

===NH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:NH3_optimisation_summarytable.png]]

'''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
Predicted change in Energy=-9.843883D-11
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3_FREQ.log| OLIVIAPINI_NH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:Oliva_Pini_NH3BH3_summarytable.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000799 0.001800 YES
RMS Displacement 0.000401 0.001200 YES
Predicted change in Energy=-4.375842D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_NH3BH3_FREQ.log| OLIVIAPINI_NH3BH3_FREQ.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0013 -0.0012 0.0006 20.2661 23.7950 39.7039
Low frequencies --- 266.0768 632.8452 639.9192
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_NH3BH3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===Energy===

E(NH3)= -56.55777 a.u.

E(BH3)= -26.61532 a.u.

E(NH3BH3)= -83.22469 a.u.

Association energy:

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22469) - [(-56.55777) + (-26.61532)] = -0.0518 a.u. = -136 KJ/mol

This bond can be said to be of medium strength when compared to the C-C bond in isoelectronic ethane, which has a bond strength of 346 kJ/mol, as there is a difference of 210 KJ/mol.

REFERENCE: https://ch301.cm.utexas.edu/section2.php?target=thermo/thermochemistry/enthalpy-bonds.html

==Using a mixture of basis-sets and psuedo-potentials - Create a Molecule of BBr3==
===BBr3===

'''Method''' : B3LYP

'''Basis set''' : 6-31G(d,p)LANL2DZ

'''Summary Table''' :

[[File:OliviaPini_BBr3_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000116 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-3.341339D-09
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' :
Frequency file published on Dspace:

{{DOI|10042/202423}}

Frequency file from Gaussian:

[[Media:OliviaPini_BBr3_outputfile_frequency_4.log| OliviaPini_BBr3_outputfile_frequency_4.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -0.0126 -0.0064 -0.0047 2.6412 2.6412 4.9503
Low frequencies --- 155.9599 155.9619 267.6868
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OliviaPini_BBr3_outputfile_frequency_4.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_benzene_summary_table.png]]

'''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
Predicted change in Energy=-4.246203D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BENZENE_SYM_OPT_3.log| OLIVIAPINI_BENZENE_SYM_OPT_3.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0042 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BENZENE_SYM_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

'''Method''' : B3LYP

'''Basis set''' : 6-31G

'''Summary Table''' :

[[File:OliviaPini_borazine_summary_table.png]]

'''Item Table''' :

<pre>
Item Value Threshold Converged?
Maximum Force 0.000083 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000238 0.001800 YES
RMS Displacement 0.000071 0.001200 YES
Predicted change in Energy=-8.544777D-08
Optimization completed.
-- Stationary point found.
</pre>

'''Frequency File''' : Frequency file: [[Media:OLIVIAPINI_BORAZINE_FREQUENCY_2.log| OLIVIAPINI_BORAZINE_FREQUENCY_2.log]]

'''Low Frequencies''' :

<pre>
Low frequencies --- -6.7608 -6.7277 -6.2964 -0.0097 0.0561 0.1335
Low frequencies --- 289.2382 289.2486 403.7829
</pre>

'''Jmol dynamic image''' :

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>OLIVIAPINI_BORAZINE_FREQUENCY_2.log</uploadedFileContents>
</jmolApplet></jmol>

===MO Comparisons===

{| class="wikitable"
|+
|-
|Benzene Orbital || Borazine Orbital || Comaprison ||
|-
|[[File:OliviaPiniBenzeneMO14.png]]
|[[File:OliviaPiniBorazineMO15.png]]
|This is MO14 in benzene and MO15 in borazine and so the one is benzene is lower in energy however they share the same bonding pattern. In both cases this is a sigma bonding orbital with the lobes being created by the in-phase overlap of p-orbitals on the c atoms in the plane of the ring. Therefore, in both the MOs, the nodes are actually the nodes within the p-orbitals themselves and so are less significant, making these orbitals bonding. There is no significant differences between the two as in both cases there is the overlap or similarly sized 2p orbitals.
|-
|[[File:OliviaPiniBenzeneMO17.png]]
|[[File:OliviaPiniBorazineMO17.png]]
|This is MO17 in both benzene and borazine and is the lowest energy pi totally bonding pi orbital. In both cases this is the in phase overlap of 2p orbitals out of the plane of the of the ring, forming a cloud of electron density above and below the plane of the atoms. In benzene the electron cloud is symmetric and totally localized over all the atoms. Whereas in borazine there is a less symmetric electron distribution, with more electron density being on the nitrogen, which is expected as it is more electronegative then boron.
|-
|[[File:OliviaPiniBenzeneMO20.png]]
|[[File:OliviaPiniBorazineMO20.png]]
|This is MO20 in both cases, representing one of the degenerate HOMO orbitals. This is overall a bonding orbital, however it does have anti-bonding character as there is a node in both orbitals going down in between the two clouds of electron density. This is a significant node as it is not due to a node within an atomic orbitals. These orbitals are formed by the two set of adjacent carbons having in phase overlap of their 2p orbitals above and below the plane of the ring. The two bonding overlaps are antibonding in respect to eachother, however as this interaction occurs over a larger distance it is weaker and the overall orbital is bonding. Again the borazine orbital is less symmetric then the benzene one, with more electron density being on the more electronegative nitrogen again.
|}

==Charge Distribution analysis==

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|C
|(-0.239)
|-
|H
|(0.239)
|}
''Table x: Charge Distribution in benzene.''

{| class="wikitable"
|+
|-
|Atom || Charge Distribution
|-
|N
|(-1.102)
|-
|B
|(0.747)
|-
|H(attached to B)
|(-0.077)
|-
|H(attached to N)
|(0.432)
|}
''Table x: Charge Distribution in borazine.''