ChemWiki - User contributions [en]

Rep:Mod:jl10312

2015-03-13T03:16:15Z

Jl10312: /* Effects of Substituition */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the pz-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

These MOs are in fact very similar to those described in Comparison 1. The major difference between them is that the orbital involved are the s-orbitals and not the p-orbitals. The same rationales used before can be used again here to explain the depiction of the orbitals as well as the energies of the orbitals which are considerably lower in energy because the MOs are comprised of lower energy s-orbitals. The most interesting aspect of these MOs is that the orbitals are considerably more diffuse than that suggested by LCAO. The s-orbitals also appear to fill across the centre of molecule rather than localised simply along the sigma framework. This perhaps suggests there may be some contribution of this MO to the delocalisation of electrons in the aromaticity.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.24960
| 0.01094
| -0.50847
| -0.27590
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system with exception to pyridinium. Firstly we can describe this MO of benzene with a LCAO approach. The MO consists of perpendicular pz orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet.

The orbital composition of this MO is similar to that described in Comparison 2 with only p-orbitals present. However, this MO has an additional anti-bonding interaction and therefore the energy of this orbital is slightly higher and computed to be -0.24690. The energy of the boratabenzene HOMO is 0.01095, higher than the HOMO of benzene and slightly positive making it anti-bonding. This high energy HOMO therefore makes boratabenzene more prone to electrophilic attack. The fact that it is anti-bonding also explains the larger orbital surface around the boron atom despite it being more electropositive. Because the energy of this MO is so high, it is closer in energy to the boron orbital fragment and therefore possesses greater character from this fragment. Next, it should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The other associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO and involves only the p-orbitals from 4 carbons. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen. Considering this, the broken degeneracy of boratabenzene can also be explained. However, the contribution of the boron atom results in the MO being pushed up in energy to the HOMO instead of down with the nitrogen. We are in reality describing the same MO despite the difference in their order.

Finally for borazine, the imbalance between the orbital surfaces on both sides of the molecule is again explained by different contributions from the orbital fragments that define the MO in the LCAO. Because the orbital fragments are asymmetrical, one fragment possesses two stabilising nitrogens compared to only one on the other. The fragment with two nitrogens is therefore lower in energy and has a greater contribution to the MO. This is why the orbital lobe on one side of the nodal plane is larger than on the other.

=== Effects of Substituition ===

As has widely been discussed thus far, minute alterations of the structure of the benzene molecule leads to a change in the MOs. These alterations arise out of the presence of different atoms in the molecule but also the resulting optimised geometries these atoms impose. This is clearly demonstrated by the geometry data collected from the optimisations of the 4 molecules performed earlier:

{| class="wikitable"
|+ Geometry Data
! !! Benzene !! Boratazene !! Pyridinium !! Borazine
|-
| r(C-H) Å || 1.09 || n/a || n/a || n/a
|-
| r(B-H) Å || n/a || 1.22 || n/a || 1.19
|-
| r(N-H) Å || n/a || n/a || 1.02 || 1.01
|-
| r(B-N) Å || n/a || n/a || n/a || 1.43
|-
| r(C-C) Å || 1.40 || n/a || n/a || n/a
|-
| r(C1,5-H) Å || n/a || 1.10 || 1.08 || n/a
|-
| r(C2,4-H) Å || n/a || 1.10 || 1.08 || n/a
|-
| r(C3-H) Å || n/a || 1.09 || 1.09 || n/a
|-
| r(N-C1,5) Å || n/a || n/a || 1.35 || n/a
|-
| r(B-C1,5) Å || n/a || 1.51 || n/a || n/a
|-
| r(C1,5-C2,4) Å || n/a || 1.40 || 1.38 || n/a
|-
| r(C2,4-C3) Å || n/a || 1.41 || 1.40 || n/a
|-
| θ(C-C-C) degrees(º) || 120 || n/a || n/a || n/a
|-
| θ(B-N-B) degrees(º) || n/a || n/a || n/a || 123
|-
| θ(N-B-N) degrees(º) || n/a || n/a || n/a || 117
|-
| θ(C2-C3-C4) degrees(º) || n/a || 120 || 120 || n/a
|-
| θ(C3-C2,4-C1,5) degrees(º) || n/a || 122 || 119 || n/a
|-
| θ(C2,4-C1,5-B) degrees(º) || n/a || 120 || n/a || n/a
|-
| θ(C1,5-N-C5,1) degrees(º) || n/a || n/a || 123 || n/a
|-
| θ(H-C/H-N/H-B) degrees(º) || 180 || 180 || 180 || 180
|}

This change in geometry ultimately affects the point group allocation of the molecule:

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As a result of the variation of point group, the MOs formed for these molecules will differ in symmetry labels and so will also have different structures as has been evident in the comparisons carried out above.

As was described in Comparison 3 for boratabenzene and pryidinium, disruption of the symmetry can result in the disruption of degenerate orbitals. The orbitals compared are originally degenerate in benzene but due to the change in symmetry, the molecules are no longer degenerate and have different energies. This disruption may also affect the reactivity of a molecule as the ordering of the orbitals may influence which orbital eventually becomes the HOMO.

Rep:Mod:jl10312

2015-03-13T02:51:58Z

Jl10312: /* MO Comparison */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the pz-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

These MOs are in fact very similar to those described in Comparison 1. The major difference between them is that the orbital involved are the s-orbitals and not the p-orbitals. The same rationales used before can be used again here to explain the depiction of the orbitals as well as the energies of the orbitals which are considerably lower in energy because the MOs are comprised of lower energy s-orbitals. The most interesting aspect of these MOs is that the orbitals are considerably more diffuse than that suggested by LCAO. The s-orbitals also appear to fill across the centre of molecule rather than localised simply along the sigma framework. This perhaps suggests there may be some contribution of this MO to the delocalisation of electrons in the aromaticity.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.24960
| 0.01094
| -0.50847
| -0.27590
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system with exception to pyridinium. Firstly we can describe this MO of benzene with a LCAO approach. The MO consists of perpendicular pz orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet.

The orbital composition of this MO is similar to that described in Comparison 2 with only p-orbitals present. However, this MO has an additional anti-bonding interaction and therefore the energy of this orbital is slightly higher and computed to be -0.24690. The energy of the boratabenzene HOMO is 0.01095, higher than the HOMO of benzene and slightly positive making it anti-bonding. This high energy HOMO therefore makes boratabenzene more prone to electrophilic attack. The fact that it is anti-bonding also explains the larger orbital surface around the boron atom despite it being more electropositive. Because the energy of this MO is so high, it is closer in energy to the boron orbital fragment and therefore possesses greater character from this fragment. Next, it should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The other associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO and involves only the p-orbitals from 4 carbons. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen. Considering this, the broken degeneracy of boratabenzene can also be explained. However, the contribution of the boron atom results in the MO being pushed up in energy to the HOMO instead of down with the nitrogen. We are in reality describing the same MO despite the difference in their order.

Finally for borazine, the imbalance between the orbital surfaces on both sides of the molecule is again explained by different contributions from the orbital fragments that define the MO in the LCAO. Because the orbital fragments are asymmetrical, one fragment possesses two stabilising nitrogens compared to only one on the other. The fragment with two nitrogens is therefore lower in energy and has a greater contribution to the MO. This is why the orbital lobe on one side of the nodal plane is larger than on the other.

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T02:46:12Z

Jl10312: /* Comparison 3 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the pz-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.24960
| 0.01094
| -0.50847
| -0.27590
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system with exception to pyridinium. Firstly we can describe this MO of benzene with a LCAO approach. The MO consists of perpendicular pz orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet.

The orbital composition of this MO is similar to that described in Comparison 2 with only p-orbitals present. However, this MO has an additional anti-bonding interaction and therefore the energy of this orbital is slightly higher and computed to be -0.24690. The energy of the boratabenzene HOMO is 0.01095, higher than the HOMO of benzene and slightly positive making it anti-bonding. This high energy HOMO therefore makes boratabenzene more prone to electrophilic attack. The fact that it is anti-bonding also explains the larger orbital surface around the boron atom despite it being more electropositive. Because the energy of this MO is so high, it is closer in energy to the boron orbital fragment and therefore possesses greater character from this fragment. Next, it should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The other associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO and involves only the p-orbitals from 4 carbons. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen. Considering this, the broken degeneracy of boratabenzene can also be explained. However, the contribution of the boron atom results in the MO being pushed up in energy to the HOMO instead of down with the nitrogen. We are in reality describing the same MO despite the difference in their order.

Finally for borazine, the imbalance between the orbital surfaces on both sides of the molecule is again explained by different contributions from the orbital fragments that define the MO in the LCAO. Because the orbital fragments are asymmetrical, one fragment possesses two stabilising nitrogens compared to only one on the other. The fragment with two nitrogens is therefore lower in energy and has a greater contribution to the MO. This is why the orbital lobe on one side of the nodal plane is larger than on the other.

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T02:20:00Z

Jl10312: /* Comparison 2 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the pz-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.24960
| -0.01094
| -0.50847
| -0.27590
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system with exception to pyridinium. Firstly we can describe this MO of benzene with a LCAO appaorach. The MO consists of perpendicular pz orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet.

The orbital composition of this MO is similar to that described in Comparison 2 with only p-orbitals present. However, this MO has an additional anti-bonding interaction and therefore the energy of this orbital is slightly higher and computed to be -0.24690. The energy of the Boratabenzene HOMO is 0.01095, higher than the HOMO of benzene making this molecule more susceptible to electrophilic attack. The same nodal planes remain. The HOMO in pyridinium is at an energy of -0.47886 making this more stable than benzene, its seems from the computed MO that the ordering of MO’s has perhaps changed, a LCAO using only 4 perpendicular p orbitals could be used to construct this MO. The lower energy of this homo makes it very unreactive towards electrophiles, as expected for a positively charged species.

It should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen.

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T02:19:25Z

Jl10312: /* Comparison 3 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.24960
| -0.01094
| -0.50847
| -0.27590
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system with exception to pyridinium. Firstly we can describe this MO of benzene with a LCAO appaorach. The MO consists of perpendicular pz orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet.

The orbital composition of this MO is similar to that described in Comparison 2 with only p-orbitals present. However, this MO has an additional anti-bonding interaction and therefore the energy of this orbital is slightly higher and computed to be -0.24690. The energy of the Boratabenzene HOMO is 0.01095, higher than the HOMO of benzene making this molecule more susceptible to electrophilic attack. The same nodal planes remain. The HOMO in pyridinium is at an energy of -0.47886 making this more stable than benzene, its seems from the computed MO that the ordering of MO’s has perhaps changed, a LCAO using only 4 perpendicular p orbitals could be used to construct this MO. The lower energy of this homo makes it very unreactive towards electrophiles, as expected for a positively charged species.

It should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen.

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T02:14:08Z

Jl10312: /* Comparison 3 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.24960
| -0.01094
| -0.50847
| -0.27590
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system with exception to pyridinium. Firstly we can describe this MO of benzene with a LCAO appaorach. The MO consists of perpendicular px orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet.

The energy of this orbital is computed to be -0.24690. The energy of the Boratabenzene HOMO is 0.01095, higher than the HOMO of benzene making this molecule more susceptible to electrophilic attack. The same nodal planes remain. The HOMO in pyridinium is at an energy of -0.47886 making this more stable than benzene, its seems from the computed MO that the ordering of MO’s has perhaps changed, a LCAO using only 4 perpendicular p orbitals could be used to construct this MO. The lower energy of this homo makes it very unreactive towards electrophiles, as expected for a positively charged species.

It should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen.

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:44:16Z

Jl10312: /* Comparison 3 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 21st
| 21st
| 20th
| 21st
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

This MO under consideration is the HOMO of each system. That of benzene's can be depicted with a LCAO of perpendicular px orbitals on each member of the ring where three orbitals on each side are in phase with one another but not with respect to the three orbitals on the other side. As a result of this, an additional nodal plane is present perpendicular to the plane of the ring where the two triplets of orbitals meet. The energy of this orbital is computed to be -0.24690. The energy of the Boratabenzene HOMO is 0.01095, higher than the HOMO of benzene making this molecule more susceptible to electrophilic attack. The same nodal planes remain. The HOMO in pyridinium is at an energy of -0.47886 making this more stable than benzene, its seems from the computed MO that the ordering of MO’s has perhaps changed, a LCAO using only 4 perpendicular p orbitals could be used to construct this MO. The lower energy of this homo makes it very unreactive towards electrophiles, as expected for a positively charged species.

It should be noted that this MO for pyridinium has in fact been reordered. In benzene, the HOMO consists of two degenerate MOs. In the instance of pyridinium, the MO in consideration is not in fact the HOMO as a result of the degeneracy that has been broken. It is the 20th MO as a result of participation of the nitrogen heteroatom orbital fragment to the final MO and therefore the energy is lowered. The associated degenerate orbital in benzene excludes two carbon fragment contributions to the MO. In the case of pyridinium, one of the two atoms excluded from contributing to the final MO is the nitrogen. This MO therefore does not benefit from the low energy nitrogen.

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:28:20Z

Jl10312: /* Comparison 2 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13210
| -0.64064
| -0.36129
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.13210 AU than that of benzene at -0.35994 AU. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.64064 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.36129, similar to benzene.

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:23:16Z

Jl10312: /* Comparison 1 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:22:29Z

Jl10312: /* Comparison 1 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. As a result of this, a nodal plane is found in the place of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.51956 AU than that of benzene at -0.74000. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.99321 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.83516 AU. It is found closer in energy to pyridinium than it is to boratabenzene relative to benzene because N is considerably more electronegative to carbon than boron is electropositive to carbon.

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:21:34Z

Jl10312: /* Comparison 1 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. This is also explained by the relative energies of boron and carbon in an orbital diagram. As this is a bonding MO in consideration, the boron orbital fragments, which is less electronegative, will be higher in energy and therefore contribute less to final bonding MO. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Once again, the contribution to the final bonding MO will be greater from the nitrogen orbital fragment as it is more electronegative and lower in energy. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.51956 AU than that of benzene at -0.74000. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.99321 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.83516 AU. It is found closer in energy to pyridinium than it is to boratabenzene relative to benzene because N is considerably more electronegative to carbon than boron is electropositive to carbon.

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:15:54Z

Jl10312: /* MO Comparison */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.51956 AU than that of benzene at -0.74000. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.99321 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.83516 AU. It is found closer in energy to pyridinium than it is to boratabenzene relative to benzene because N is considerably more electronegative to carbon than boron is electropositive to carbon.

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T01:14:43Z

Jl10312: /* MO Comparison */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.84671
| -0.06437
| 1.21402
| -0.88851
|-
| Order
| 7th
| 7th
| 7th
| 7th
|-
| Degenerate?
| No
| No
| No
| No
|}

This set of MOs depict the delocalised π system described before. In all cases, only the px-orbitals of the 6 members of the ring are involved, found above and below the plane of the ring. The interaction between the 6 members is the through space bonding of the in phase lobes of the orbitals. No anti-bonding components are involved.

The shapes of the orbitals are all fairly similar with the differences between them being the skewing of the orbital lobes in certain directions, towards certain atoms. The skewing is easily explained by the charge distribution describe before. In the case of benzene, the surface describing the orbitals is uniform due to the high symmetry. In the case of boratabenzene, electron density is skewed away from the electropositive boron atom and this is show by the boron in the depiction being slightly exposed. In contrast, the orbital surface for pyridinium is skewed toward and thickest at the highly electronegative nitrogen atom leaving the carbons on the opposite end of the ring exposed. Such is the extent of this polarisation and build up of electron density at nitrogen that the hydrogen bound to the nitrogen appears to have an orbital contribution of its own to the overall MO. This is, in reality, not the case. Finally, for borazine, the orbitals are in effect a superposition of the MOs at the B-H and N-H units of boratabenzene and pyridinium respectively and is almost an exact representation of the charge distribution described before in the NBO analysis.

The energies of each MO can also be explained by the same rationale employed when describing the orbital surfaces. Boron is more electropositive than carbon, the MO is therefore higher in energy at -0.51956 AU than that of benzene at -0.74000. Conversely for nitrogen, the high electronegativity stabilises the molecule and brings the energy down to -0.99321 AU. In the case of borazine, the effects of the heteroatoms once again combine to cancel each other out and is therefore found somewhere between boratabenzene and pyridinium at -0.83516 AU. It is found closer in energy to pyridinium than it is to boratabenzene relative to benzene because N is considerably more electronegative than carbon than boron is electropositive to carbon.

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T00:51:06Z

Jl10312: /* NBO Charge Analysis */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-13T00:38:30Z

Jl10312: /* NBO Charge Analysis */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

The key property at the heart of all discussions on charge distribution within a molecule is the electronegativity of the constituent atoms. Electronegativity is often simply defined as an atom's affinity for a pair of electrons in a covalent bond. This is important in this context as all molecules in consideration are organic molecules containing intramolecular covalent bonding between the atoms via, as what has been emphasised thus far, orbital interactions. According to the Pauling Scale, the electronegativity values for the 4 types of atoms involved are 2.20, 2.55, 2.04 and 3.04 for H, C, B and N respectively.

Firstly, we will look at benzene as a reference and as a standard moiety to study the cyclic, aromatic properties of the systems. Benzene is perfectly symmetrical with 6 carbons bound together in a ring via 6 sigma C-C bonds. Each carbon is also bound to one hydrogen. Additionally, each carbon is sp2 hybridised and possesses a single unpaired electron in the remaining un-hybridised p-borbital orthogonal to the ring. These 6 single unpaired electrons are then delocalised in the ring resulting in an aromatic compound. Due to its symmetry, benzene has a uniform distribution of electronic charge; This is to say, each carbon possesses the same charge as every other. his is similarly the case for the hydrogens. It is observed that the carbons possess a lower electronic charge density than the hydrogens. This is in agreement with carbon being more electronegative as well as the high electron density as a result of the delocalised electrons in the ring.

When moving from benzene to boratabenzene, one of the carbons of the ring is substituted with a boron atom. Hence,the element of symmetry is loss and the uniform distribution of electronic charge across the carbons is lost. Boron is less electronegative than both carbon and hydrogen. Immediately, we may observe that the boron atom of the molecule possesses the lowest charge density of 0.202 (ie. the most electropositive value) compared to all the constituent atoms in the molecule. Subsequently, we can see that there is significant build up of negative charge on the carbons of the ring, in particular at the ortho- (-0.588) and para- (-0.348) positions. This is not surprising as carbon is the most electronegative atom in this system. The build of charge at the two positions mentioned is a result of the formal negative charge of the molecule which can be pushed around the ring. A series of resonance forms describing this process will clearly demonstrate the build up of charge at these positions. Consequently, the hydrogens bound at these positions are comparably more electropositive than those at the other positions. It is noted that the hydrogens bound to the carbons are once again electropositive as was the case in benzene. However, for the reason just described the result is that some variation in the values between the hydrogens is also present. Most notably, the hydrogen bound to the boron atom actually possesses a slightly negative value of -0.096. This is because in this instance, hydrogen is actually more electronegative than the boron and therefore holds a higher share of the electron density.

When moving from benzene to pyridinium, one of the carbons of the ring is substituted with a nitrogen atom instead. Similarly with boratabenzene, the symmetry of the molecule is loss and as expected, the distribution of charge across the molecule will once again be affected. Nitrogen is considerably more electronegative than the 3 atoms previously discussed. Therefore, one observes that it possesses a great deal of the electron density with a value of -0.476. As with boratabenzene before, a series of resonance structures pushing the formal positive charge around the ring will demonstrate a build up of delta positive charge at the ortho- and para- positions. It is therefore unsurprising that this is where the carbons in possession of the least amount of negative charge are found with values of -0.122 and 0.071. In contrast to the hetereoatom-bound hydrogen in boratazene, that of pyridinium possesses an exceptionally high electropositive charge of 0.483. This is testament to the high electronegativity of nitrogen which pulls a lot of the charge density from the hydrogen. Again, the remaining hydrogens possess charge density values in reflection of the carbons they are bound to as well as the break in symmetry.

Borazine varies from benzene in that the 6 membered ring alternating between boron and nitrogen atoms and each similarly bound to a hydrogen. From the above discussion, it is unsurprising to observe the polarisation of electron density at the nitrogens (-1.102) leaving considerable electropositive build up on the borons (0.747). As with the heteroatom-bound hydrogens before, those bonded to nitrogens possess an overall electropositive charge (0.432) and those bonded to borons with an overall electronegative charge distribution (-0.077).

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T23:05:40Z

Jl10312: /* Effects of substituition */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

=== Effects of Substituition ===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T23:05:10Z

Jl10312: /* NBO Charge Analysis */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

=== NBO Charge Analysis ===

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T23:03:04Z

Jl10312:

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -135.6 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:59:40Z

Jl10312: /* Frequency Analysis for NH3BH3 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = -152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:56:09Z

Jl10312: /* = Comparison 3= */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:55:57Z

Jl10312: /* = Comparison 2= */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:55:38Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.01
|-
| r(B-H) Å || 1.19
|-
| r(B-N) Å || 1.43
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:55:10Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.22
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:54:46Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.10
|-
| r(C2,4-H) Å || 1.10
|-
| r(C3) Å || 1.09
|-
| r(B-C1,5) Å || 1.51
|-
| r(C1,5-C2,4) Å || 1.40
|-
| r(C2,4-C3) Å || 1.41
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:54:08Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.02
|-
| r(C1,5-H) Å || 1.08
|-
| r(C2,4-H) Å || 1.08
|-
| r(C3-H) Å || 1.09
|-
| r(N-C1,5) Å || 1.35
|-
| r(C1,5-C2,4) Å || 1.38
|-
| r(C2,4-C3) Å || 1.40
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:52:54Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.09
|-
| r(C-C) Å || 1.40
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:52:20Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.02
|-
| r(N-H) Å || 1.21
|-
| r(B-N) Å || 1.67
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.0864
|-
| r(C-C) Å || 1.3963
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:51:46Z

Jl10312: /* Geometry Data */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.02
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.0185
|-
| r(N-H) Å || 1.2098
|-
| r(B-N) Å || 1.6677
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.0864
|-
| r(C-C) Å || 1.3963
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

Rep:Mod:jl10312

2015-03-12T22:48:58Z

Jl10312: /* MO Comparison */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.0180
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.0185
|-
| r(N-H) Å || 1.2098
|-
| r(B-N) Å || 1.6677
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.0864
|-
| r(C-C) Å || 1.3963
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==== NBO Charge Analysis ====

{| class="wikitable" border="1"
|+ NBO Data '''(1.102 - +1.102 colour limits)'''
! Benzene !! Boratabenzene !! Pyridinium !! Borazine
|-
| [[File:JL Benzene NBOAnalysis Clean.PNG|300px]] || [[File:JL Borataenzene NBOAnalysis Clean.PNG|300px]] || [[File:JL_Pyridinium NBOAnalysis Clean.PNG|300px]] || [[File:JL Borazine NBOAnalysis Clean.PNG|300px]]
|}

Differences in the electron density on each atom can be explained by the atom's electronegativity – its tendency to attract and its affinity for a pair of electrons.
Benzene being symmetric has uniform electron density over all its carbon and hydrogen atoms respectively. From the figure above we can see that the carbon atoms in benzene have a charge of -0.239 with the hydrogen’s exhibiting a charge of equal and opposite magnitude. This confirms that the carbon is in fact more electronegative than hydrogen, confirmed by the Pauling scale of electronegativity. Literature values on the Pauling scale show an E-neg difference of 0.350 for Carbon relative to hydrogen, this is consistent with the NBO charge distribution computed from our optimised structure.

When we move from Boron to Boratabenzene we reduce some symmetry and the remaining carbons no longer have an equally disturbed level of electron density. Boron is less electronegative than both Carbon and Hydrogen. The Carbon atoms within the ring have an even larger affinity for electron density relative to boron atoms. The interesting point it notice is that, the Carbon atoms adjacent to the Boron are more negatively charged than previously. The para carbon is also more negatively charged at a value of -0.348 in comparison to its adjacent carbons at -0.250 (meta). This could be explained by the fact that there is a formal negative charge on this complex. This negative charge could be alternating on the othro and meta positions, easily shown by resonance forms of this anion.

The isoelectronic pyridinium contains the most electronegative atom in our any of our three benzene analogues. It is expected that the nitrogen atom has the largest negative charge of any atom in within the cation, the NBO analysis confirms this, the value being -0.476. In contrast to Boratabenzene, pyrdinium carries a net positive +1 charge. In this case the carbons at position 3 and 5 are have a charge value of -0.241, whilst the position 2 and 4 are more positive at 0.071 and -0.122. The position adjacent to the Nitrogen is the most positive carbon due to its close proximity to the nitrogen atom, but also because resonance forms can formally place the net +1 charge at the positions 2, 6 and 4 (othro and para).

Borazine has a highly symmetric nature due to alternating electronegative nitrogen and electropositive Boron atoms. With the very large electronegativity gap between these atoms we should expect these nitrogen atoms to be the most electron density rich and the adjacent boron atoms to been the most electron density poor atoms across all four molecules, and this is certainly the case. The charge colour diagrams clearly represent this. On Borazine, the nitrogen atoms have a value of -1.102 whilst the alternating boron atoms have a value of 0.747.

=== MO Comparison ===

==== Comparison 1 ====

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 2= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

==== Comparison 3= ===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

File:JL Borazine NBOAnalysis Clean.PNG

2015-03-12T22:47:05Z

Jl10312:

File:JL Pyridinium NBOAnalysis Clean.PNG

2015-03-12T22:46:44Z

Jl10312:

File:JL Borataenzene NBOAnalysis Clean.PNG

2015-03-12T22:46:23Z

Jl10312:

File:JL Benzene NBOAnalysis Clean.PNG

2015-03-12T22:45:58Z

Jl10312:

Rep:Mod:jl10312

2015-03-12T22:39:43Z

Jl10312: /* Comparison 3 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.0180
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.0185
|-
| r(N-H) Å || 1.2098
|-
| r(B-N) Å || 1.6677
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.0864
|-
| r(C-C) Å || 1.3963
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==MO Comparison==

===Comparison 1===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

===Comparison 2===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

===Comparison 3===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(21) 1.PNG|250px]]
| [[File:Boratabenzene MO(21) 1.PNG|250px]]
| [[File:Pyridinium MO(21) 1.PNG|250px]]
| [[File:Borazine MO(21) 1.PNG|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

File:Borazine MO(21) 1.PNG

2015-03-12T22:38:36Z

Jl10312:

File:Pyridinium MO(21) 1.PNG

2015-03-12T22:38:15Z

Jl10312:

File:Boratabenzene MO(21) 1.PNG

2015-03-12T22:37:48Z

Jl10312:

File:Benzene MO(21) 1.PNG

2015-03-12T22:37:22Z

Jl10312:

Rep:Mod:jl10312

2015-03-12T22:36:43Z

Jl10312: /* Comparison 2 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.0180
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.0185
|-
| r(N-H) Å || 1.2098
|-
| r(B-N) Å || 1.6677
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.0864
|-
| r(C-C) Å || 1.3963
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==MO Comparison==

===Comparison 1===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

===Comparison 2===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(17) 3.PNG|250px]]
| [[File:Boratabenzene MO(17) 3.PNG|250px]]
| [[File:Pyridinium MO(17) 3.PNG|250px]]
| [[File:Borazine MO(17) 1.PNG|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

===Comparison 3===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:NM Benzene comp 3 MO.jpg|250px]]
| [[File:NM Boratabenzene comp 3 MO.jpg|250px]]
| [[File:NM Pyridium comp 3 MO.jpg|250px]]
| [[File:NM Borazine comp 3 MO.jpg|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This molecular orbital shows the delocalised π system,. It constitutes entirely of px orbitals found above and below the plane of the ring giving in phase strong through space bonding with no anti bonding component present.

The calculated MOs for all four molecules show a very similar shape with the only differences being a bulging of the orbital around the respective electronegative parts of the molecule: the carbon in the four position in boratabenzene and the nitrogen atoms found in pyridinium and borazine. This is to be expected as more electronegative atoms draw electron density closer to themselves.

The relative energies of the orbitals can be explained in a similar fashion to the orbitals in Comparison 2 in that boron and nitrogen destabilise and stabilise respectively and the symmetry of the borazine atom allows for balance between these effects.

The orbitals all have the same order (17th) which is due to this orbital's contribution to the aromaticity of the molecule which is why there are also no degenerate orbitals present in each molecule.

Where the LCAO suffers in its predictive ability is that it is unable to determine how much each atom's px orbital will contribute to the overall molecular orbital, however knowledge of electronegativities does make this possible to predict without the use of LCAO. All in all, this is a further demonstration of why it is important to calculate the MOs rather than relying on LCAO theory.

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

File:Borazine MO(17) 1.PNG

2015-03-12T22:35:47Z

Jl10312:

File:Pyridinium MO(17) 3.PNG

2015-03-12T22:34:47Z

Jl10312:

File:Boratabenzene MO(17) 3.PNG

2015-03-12T22:32:29Z

Jl10312:

File:Benzene MO(17) 3.PNG

2015-03-12T22:32:09Z

Jl10312:

File:Boratabenzene MO(17) 1.PNG

2015-03-12T22:31:29Z

Jl10312:

File:Benzene MO(17) 1.PNG

2015-03-12T22:31:04Z

Jl10312:

Rep:Mod:jl10312

2015-03-12T22:30:40Z

Jl10312: /* Comparison 1 */

== Inorganic Computational Laboratory ==

== Day 1 ==

The purpose of the first part of the computational laboratory is to optimise several molecules so that they may be compared in subsequent parts of this exercise. Molecules are optimised by Gaussview using the B3LYP method and various input basis sets. A molecule is optimised when its ideal energy, as interpreted by Gaussview, is achieved ie. when Gaussview is able to minimise the potential energy (find the most negative energy value with the smallest gradient close to zero) of the molecule. The molecule is in its equilibrium geometry!

==== Optimisation of BH3 ====

Initially, the bond lengths of each B-H bond were intentionally offset as 1.53, 1.54 and 1.55 Å respectively while conserving the trigonal planar geometry of the molecule. An optimisation was subsequently carried out.

Optimisation file of BH3 with 3-21G basis set can be found [[Media:JL_BH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 3-12G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| r(B-H) Å || 1.19
|-
| θ(H-B-H) degrees(º) || 120
|}

It is observed that despite the initial offset of the bond lengths, the optimisation of the molecule has equalised the bond lengths of each B-H bond to 1.19 Å.

== Day 2 ==

==== Optimisation of BH3 ====
Optimisation file of BH3 with 6-31G(d,p) basis set can be found [[Media:JL_BH3_OPT_DAY2_631G_DP.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 with 6-31G (d,p) Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BH3_Opt_Day2_631g_dp_ResultsSummary.png|300px]]
| [[File:JL_BH3_OptimisedConvergence_Day2_631G_DP.png]]
| <jmol><jmolApplet>
<title> BH3 Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BH3_Opt_Day2_631g_dp.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of GaBr3 ====
Optimisation file of GaBr3 with LANL2DZ basis set can be found [[Media:JL_GaBr3_pp_optimisation.log.log| here]]. {{DOI|10042/195225}}

{| class="wikitable" border="1"
|+ Optimised GaBr3 with LANL2DZ Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_GaBr3_pp_Opt_ResultsSummary.png|300px]]
| [[File:JL_GaBr3_Day2_LANDL2DZ_OptimisedConvegence.png]]
| <jmol><jmolApplet>
<title> GaBr3 Optimised LANDL2DZ</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_GaBr3_pp_optimisation.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Optimisation of BBr3 ====
Optimisation file of BBr3 with GEN basis set can be found [[Media:JL_BBr3_OPT_DAY2_GEN.log| here]]. {{DOI|10042/195231}}

{| class="wikitable" border="1"
|+ Optimised BBr3 with GEN Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_BBr3_Opt_Day2_GEN_ResultsSummary.png|300px]]
| [[File:JL_BBr3_Day2_GEN_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> BBr3 Optimised GEN</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BBr3_OPT_DAY2_GEN.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

As evidenced by the above calculations, all molecules have been optimised and their stationary points have been found.

==== Geometry Comparison ====

{| class="wikitable"
|+ Geometry Data
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120 || 120 || 120
|}

Geometry Analysis : It is expected, purely on the rationale of increasing the size of the constituent atoms (atomic and van der waals radii), one would expect greater bond lengths between the central and surrounding atoms as we move across from BH3 to BBr3 to GaBr3. Furthermore, the bond angles would not expect to change between the three compounds as the central atoms of B and Ga are in the same group. Therefore, the overall structure of the molecule is not majorly affected as the type of bonding interaction and the directionality of orbitals involved in the bonding is the same. These postulations are indeed shown to be the case as demonstrated from the table above.

Firstly, it is observed that all bond angles are the same at 120º demonstrating that the trigonal planar geometry is preserved across all three molecules. Subsequently, Hydrogen has a significantly smaller atomic radius of 25 pm than Bromine of 115 pm. Therefore, the B-H bond length of borane will be smaller than the B-Br bond length of borontribromide because the Br atoms cannot lie closer to the central B atom. Similarly, as the central atom is changed from B to Ga, the same rationale can be applied with the atomic radius of B (85 pm) smaller than that of Ga (130 pm). This data also suggests the decreasing strengths of the bonds moving across the molecules in the table due to shorter bond lengths and therefore higher bond order. This would be expected as the less diffuse orbitals of the smaller H and B atoms have better overlap (and therefore better bonding interactions) than those of B with the larger Br orbitals. However, this is misleading may be misleading as one must also consider the electronegativity of the constituent atoms.

Br is significantly more electronegative than H. Therefore, the greater difference in electronegativity between B and Br may result in a more stable bond. This should be able to be determined by comparing the energies of each molecule but different basis sets were used in the optimisation process; These energies therefore cannot be compared. An explanation for why this is the case is given further on.
 

What is a bond? : A bond is commonly denoted by a line joining two atoms and signifies some kind of interaction between the two atoms connected by the line. The question posed is a challenging one to answer due to the variety of types of chemical bonding in existence that are unique from one another in some way. Classically, a bond can be defined as a favourable, electrostatic interaction or attraction between two atoms. Chemical bonding takes many forms and is defined by the degree to which the interactions between the atoms takes place. The simplest examples of these interactions are a result of the sharing of electrons or electron density between the atoms via orbitals (covalent bonding). The other is the outright donation of electrons from one atom to another where the attraction is between the separated charges (ionic bonding). In reality, there is a spectrum between the two types of bonding described here and where the bonding lies along the scale is determined by a combination of the size and electronegativity of the atom. A bond is considered to have formed if there is a net reduction in the potential energy of the system or molecule. This was alluded to earlier when describing the process by which Gaussview optimises molecules. However, static structures often drawn for molecules are simplifications of a more dynamic picture as bonds may vibrate within molecules. Therefore, it is an important distinction to note that what is depicted when the bonds of a molecule are drawn is simply the representation of the molecule in its equilibrium state, that with its potential energy minimised.

What has been described above is merely a simplistic summary of chemical bonding. More complex forms of chemical bonding do exist and indeed recently, Manz et al. have [http://www.rsc.org/chemistryworld/2014/10/isotope-effect-produces-new-type-chemical-bond reported an entirely new type of chemical bonding] which circumvents the need for the minimisation of the potential energy of the molecule described before by stabilisation of the vibrational zero point energy instead.
 

How much energy is there in a strong, medium and weak bond? : The two types of bonding described above, ionic and covalent, take place within molecules (intramolecular) and are often considered examples of strong types of bonding. For example, the bonding between the two nitrogens within a molecule of di-nitrogen, N2, is incredibly strong with a triple bond strength equivalent to 945 kJ mol-1, one of the strongest known. Consequently, N2 is incredibly stable and unreactive. An example of a medium bond is a simple single C-C bond of an akyl group equivalent to 348 kJ mol-1, a third that of N2. Finally, bonding between different molecules (intermolecular) such as hydrogen bonding, dipole-dipole interactions and Van der Waal's forces, are considered to be weak. This type of bonding works on the basis of the influence of the electron density or dipole moment within a given molecule on that belonging to molecules adjacent to it. Hydrogen bonding is the strongest of the three types of intermolecular bonds just listed and a single hydrogen bond is of the order of 15 kJ mol-1.
 

In some structures gaussview does not draw in the bonds where we expect, why does this NOT mean there is no bond? : Gaussview is programmed to possess a pre-determined notion of the value a bond length or a bond energy. In some cases when a poor calculation has been done or the nature of bonding is complex (such as in the instance of 3c-2e bonding), values that have been determined do not fall within the range utilised by Gaussview to determine the presence of a bond. Therefore, Gaussview will not draw the expected bond.

== Day 3 ==

==== Frequency Analysis for BH3 ====

In addition to molecule optimisation, a frequency analysis must also be undertaken in order to determine that the energy state achieved in the optimisation is indeed a minima, in which case the molecule given will be a stable species. Conversely, a zero gradient for the potential energy of a molecule may also represent a maximum, whereby the molecule is in a transient, fleeting state ie. transition state. The former scenario is desired in order to perform meaningful comparisons between the molecules. A minimum is achieved when the frequency values returned by the operation are all positive. Furthermore, the 6 low frequencies (attributed to the motion of the center of mass of the molecule) should be comparably lower than that of the remaining vibrational modes of the molecule as determined by the 3N-6 rule.

Frequency calculation for BH3 can be found [[Media:JL_BH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_BH3_frequency.png|300px]]
|
<pre>
Low frequencies --- -11.7227 -11.7148 -6.6070 -0.0010 0.0278 0.4278
Low frequencies --- 1162.9743 1213.1388 1213.1390
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1162
|93
|Yes
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|1213
|14
|Very Slight
|Bend
|-
|2583
|0
|No
|Stretch
|-
|2716
|126
|Yes
|Stretch
|-
|2716
|126
|Yes
|Stretch
|}

[[File:JL BH3 frequency IRspectrum.png|thumb|center|IR Spectrum for BH3|400px]]

It should be noted that the 3N-6 rule predicts 6 vibrational modes for a molecule of borane, BH3. However, in the infrared spectra above, only 3 peaks are observed. This result can be explained by the selection rules for infrared spectroscopy that require a change in dipole moment of the molecule upon vibration in order to be visible. Symmetrical vibrations such as that at 2583 cm-1 of BH3 do not induce a change in the dipole moment. Therefore, it would not appear in the IR spectra and is consequently not predicted by Gaussview. Fewer than 6 peaks are also not observed because some vibrations are isoenergetic and therefore degenerate with others. Therefore only a single peak, representing both vibrational modes, is observed.

==== Frequency Analysis for GaBr3 ====
Frequency calculation for GaBr3 can be found [[Media:JL_GABR3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_GaBr3_frequency_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -1.4878 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|76
|3
|Very Slight
|Bend
|-
|76
|3
|Very Slight
|Bend
|-
|100
|9
|Yes
|Bend
|-
|197
|0
|No
|Stretch
|-
|316
|57
|Yes
|Stretch
|-
|316
|57
|Yes
|Stretch
|}

[[File:JL_GaBr3_frequency_IR.png|thumb|center|IR Spectrum for GaBr3|400px]]

=== Comparison ===

The spectra for molecules are fairly similar showing 3 peaks. The reason only 3 peaks are observed in the spectra was elaborated on earlier for BH3. This is similarly the case for GaBr3. Furthermore, the number of vibrational modes are also the same as would be expected by the 3N-6 rule. Unsurprisingly, the types of each vibrations are also the same as both molecules are of the same symmetry, geometry and point group; only the constituent atoms have changed. However, there ends the similarities between frequency analyses of the molecules.

It is observed that the frequency values are considerably larger for BH3 in general as well as within each type of vibrational mode as compared to GaBr3. This is because the heavier atoms of Ga and Br vibrate slower (as a result of the change in reduced mass and force constant of the molecule) and therefore at a lower frequency than that of the lighter constituent atoms of BH3. Therefore, the frequencies associated with the vibrations of GaBr3 will be smaller. Additionally, there has also been a reordering of modes, particularly the A2" umbrella motion shown below. This vibration is lower in energy than the two degenerate bending modes for BH3 but higher for GaBr3. It would be expected that a more significant proportion of the vibration is largely attributed to the displacement of the lighter atoms in the molecule. In the case of BH3, it is the surrounding hydrogens that are responsible; for GaBr3, it is the central Ga atom. This is easily observed by the displacement vectors in the depictions below and demonstrates the reordering of modes.

{| class="wikitable" border="1"
|+
! BH3 !! GaBr3
|-
|[[File:BH3 Umbrella.PNG|300px]]||[[File:GaBr3 Umbrella.PNG|300px]]
|}

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?: The accuracy of the calculations performed by Gaussview is defined by the input basis set used. Different basis sets possess different degrees of errors associated with the calculation. If using different basis sets, the accuracy will be different and comparison of calculations between molecules is not possible.

==== Molecular Orbital Analysis for BH3 ====
{{DOI|10042/195310}}
[[File:JL BH3 MODiagram Day3.jpg|center]]

Are there any significant differences between the real and LCAO MOs? What does this say about the accuracy and usefulness of qualitative MO theory?: At a glance, it is noticeable from the MO diagram above that the MOs computed by Gaussview and those as predicted by the Linear Combination of Atomic Orbitals (LCAO) theory are in relatively good agreement. However, both approaches have their own respective drawbacks. Quantum mechanic calculations have shown that bonding orbitals often possess more character from the fragment orbitals which they are closer in energy to ie the orbital coefficient will be larger. For the orbitals computed by Gaussian, it is not easily determinable which orbital fragment has a greater orbital contribution. This is evidenced by the 2a1' bonding orbital in the diagram above where the computed orbitals blend the electron density into one another. However, for this same reason, computed orbitals are indeed more representative of the actual orbitals. Gaussian is better able to produce a space-filling model of the orbitals involved that the simple LCAO depictions cannot. This is particularly the case for the higher unoccupied bonding orbitals where the computed depictions are askew from those depicted using LCAO in order to minimise unfavourable interactions. In summary, LCAO provides a good qualitative representation of MOs from which contributions by different orbital fragments can be gauged as well as the rough ordering of the MOs. However, they do not give the most accurate representation of how MOs actually look like when the interact with each other.

==== Optimisation of NH3 ====

Optimisation file of NH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_NH3_Opt_ResultsSummary.png|300px]]
| [[File:JL_NH3_Day3_631g_dp_OptimisedConvergence.png]]
| <jmol><jmolApplet>
<title> NH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3
|-
| r(E-X) Å || 1.0180
|-
| θ(X-E-X) degrees(º) || 106
|}

==== Frequency Analysis for NH3 ====
Frequency calculation for NH3 can be found [[Media:JL_NH3_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3_frequency_Opt_ResultsSummary.png|300px]]
|
<pre>
Low frequencies --- -0.0139 -0.0035 -0.0010 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|1089
|145
|Yes
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|1694
|14
|Slight
|Bend
|-
|3461
|1
|Very Slight
|Stretch
|-
|3590
|0
|No
|Stretch
|-
|3590
|0
|No
|Stretch
|}

[[File:JL_NH3_frequency_IR.png|thumb|center|IR Spectrum of NH3|400px]]

==== NBO Analysis for NH3 ====
{{DOI|10042/195311}}

[[File:JL NH3 ChargeDistribution Day3.png|thumb|center|Charge distribution of the NBOs of NH3.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.375
|-
| N || -1.125
|}

== Day 4 ==

==== Optimisation of NH3BH3 ====
Optimisation file of NH3BH3 with 6-31G (d,p) basis set can be found [[Media:JL_NH3BH3_OPT(2)_DAY4.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised NH3BH3 Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL NH3BH3 OPT DAY4 ResultsSummary.PNG|300px]]
| [[File:JL_NH3BH3_OPT_DAY4_Convergence.PNG]]
| <jmol><jmolApplet>
<title> NH3BH3 Optimised 6-31G</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_NH3BH3_OPT_DAY4.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.0185
|-
| r(N-H) Å || 1.2098
|-
| r(B-N) Å || 1.6677
|-
| θ(H-B-H) degrees(º) || 109
|-
| θ(H-N-H) degrees(º) || 114
|-
| θ(B-N) degrees(º) || 180
|}

==== Frequency Analysis for NH3BH3 ====

Frequency calculation for NH3BH3 can be found [[Media:JL_NH3BH3_FREQUENCY(2).LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_NH3BH3_frequency_DAY4_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -5.3384 -0.3672 -0.0558 -0.0003 0.9691 1.0783
Low frequencies --- 263.2948 632.9558 638.4561
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|263
|0
|No
|Bend
|-
|633
|14
|Yes
|Stretch
|-
|638
|4
|Very Slight
|Bend
|-
|638
|4
|Very Slight
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1069
|41
|Yes
|Bend
|-
|1196
|109
|Yes
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1203
|4
|Very Slight
|Bend
|-
|1329
|114
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|1676
|28
|Yes
|Bend
|-
|2471
|67
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|2552
|231
|Yes
|Stretch
|-
|3464
|3
|Very Slight
|Stretch
|-
|3581
|28
|Yes
|Stretch
|-
|3581
|28
|Yes
|Stretch
|}

[[File:JL_NH3BH3_frequency_spectrum.PNG|thumb|center|IR Spectrum of NH3BH3|400px]]

*E(NH3) = -56.5577687 AU
*E(BH3) = -26.6153326 AU
*E(NH3BH3) = -83.2246891 AU
*ΔE = E(NH3BH3) - [E(NH3) + E(BH3)] = -0.0581878 AU = 152.78 kJ/mol
 
The calculated value of 152.78 kJ/mol tells us that the bonding interaction taking place is fairly weak relative to N2</s> and C-C described earlier.

== Project: Aromaticity ==

=== Benzene ===

==== Optimisation of Benzene ====
Optimisation file of Benzene with 6-31G (d,p) basis set can be found [[Media:JL_BENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Benzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Benzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Benzene_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Benzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Benzene_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(C-H) Å || 1.0864
|-
| r(C-C) Å || 1.3963
|-
| θ(C-C-C) degrees(º) || 120
|-
| θ(H-C) degrees(º) || 180
|}

==== Frequency Analysis for Benzene ====

Frequency calculation for Benzene can be found [[Media:JL_BENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Benzene_frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -10.2549 -5.6651 -5.6651 -0.0056 -0.0056 -0.0014
Low frequencies --- 414.5451 414.5451 621.0429
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|416
|0
|No
|Bend
|-
|416
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|621
|0
|No
|Bend
|-
|695
|74
|Yes
|Bend
|-
|718
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|865
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|975
|0
|No
|Bend
|-
|1013
|0
|No
|Bend
|-
|1018
|0
|No
|Bend
|-
|1019
|0
|No
|Stretch
|-
|1066
|3
|Yes
|Bend
|-
|1066
|3
|Yes
|Bend
|-
|1180
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1203
|0
|No
|Bend
|-
|1355
|0
|No
|Stretch
|-
|1381
|0
|No
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1524
|7
|Yes
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|1653
|0
|No
|Stretch
|-
|3172
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3181
|0
|No
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3197
|47
|Yes
|Stretch
|-
|3278
|0
|No
|Stretch
|}

[[File:JL_Benzene_frequency_Spectrum.PNG|thumb|center|IR Spectrum of Benzene|400px]]

==== Molecular Orbital Analysis for Benzene ====
{{DOI|10042/195337}}
[[File:JL Benzene MODiagram.jpg|center]]

==== NBO Analysis for Benzene ====
{{DOI|10042/195337}}

[[File:JL_Benzene_NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Benzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H || 0.239
|-
| C || -0.239
|}

*How do these MOs relate to the common conception of aromaticity? Hint 2: aromaticity relates to delocalisation. Hint 3: aromaticity relates to the total pi electron density, and MOs contain formally only 2 electrons each.

=== Boratabenzene ===

==== Optimisation of Boratabenzene ====
Optimisation file of Boratabenzene with 6-31G (d,p) basis set can be found [[Media:JL_BORATABENZENE_OPT(2).LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Boratabenzene Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL_Boratabenzene_Opt_ResultsSummary.PNG|300px]]
| [[File:JL_Boratabenzene_Opt_Congerence.PNG]]
| <jmol><jmolApplet>
<title> Boratabenzene Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_BORATABENZENE_OPT(2).mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(B-H) Å || 1.2185
|-
| r(C1,5-H) Å || 1.0968
|-
| r(C2,4-H) Å || 1.0969
|-
| r(C3) Å || 1.0915
|-
| r(B-C1,5) Å || 1.5141
|-
| r(C1,5-C2,4) Å || 1.3988
|-
| r(C2,4-C3) Å || 1.4052
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 122
|-
| θ(C2,4-C1,5-B) degrees(º) || 120
|-
| θ(C1,5-B-C5,1) degrees(º) || 115
|-
| θ(H-C/H-B) degrees(º) || 180
|}

==== Frequency Analysis for Boratabenzene ====

Frequency calculation for Boratabenzene can be found [[Media:JL_BORATABENZENE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Boratabenzene_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -7.2728 0.0008 0.0008 0.0009 3.1417 4.5184
Low frequencies --- 371.2968 404.4158 565.0833
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|371
|2
|Yes
|Bend
|-
|404
|0
|No
|Bend
|-
|565
|0
|No
|Stretch
|-
|568
|0
|No
|Bend
|-
|608
|11
|Yes
|Bend
|-
|711
|3
|Yes
|Bend
|-
|756
|7
|Yes
|Bend
|-
|814
|0
|No
|Bend
|-
|873
|3
|Yes
|Bend
|-
|906
|0
|No
|Stretch
|-
|917
|1
|Slight
|Bend
|-
|951
|0
|No
|Bend
|-
|951
|0
|No
|Bend
|-
|960
|2
|Yes
|Bend
|-
|1012
|4
|Yes
|Stretch
|-
|1085
|3
|Yes
|Bend
|-
|1175
|1
|Slight
|Bend
|-
|1180
|1
|Slight
|Bend
|-
|1227
|1
|Slight
|Stretch
|-
|1333
|31
|Yes
|Stretch
|-
|1449
|9
|Yes
|Stretch
|-
|1463
|14
|Yes
|Stretch
|-
|1565
|7
|Yes
|Stretch
|-
|1592
|40
|Yes
|Stretch
|-
|2447
|368
|Yes
|Stretch
|-
|3027
|108
|Yes
|Stretch
|-
|3038
|0
|No
|Stretch
|-
|3060
|380
|Yes
|Stretch
|-
|3061
|10
|Yes
|Stretch
|-
|3116
|112
|Yes
|Stretch
|}

[[File:JL Boratabenzene frequency Spectrum.PNG|thumb|center|IR Spectrum of Boratabenzene|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195345}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195345}}

[[File:JL Boratabenzene NBOAnalysis.png|thumb|center|Charge distribution of the NBOs of Boratabenzene.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-B) || -0.096
|-
| H(-C1,5) || 0.184
|-
| H(-C2,4) || 0.179
|-
| H(-C3) || 0.186
|-
| C1,5 || -0.588
|-
| C2,4 || -0.250
|-
| C3 || -0.340
|-
| B || 0.202
|}

=== Pyridinium ===

==== Optimisation of Pyridinium ====
Optimisation file of Pyridinium with 6-31G (d,p) basis set can be found [[Media:JL PYRIDINIUM OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Pyridinium Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Pyridinium Opt ResultsSummary.PNG|300px]]
| [[File:JL_Pyridinium_Opt_Convergence.PNG]]
| <jmol><jmolApplet>
<title> Pyridinium Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL_Pyridinium_Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0169
|-
| r(C1,5-H) Å || 1.0832
|-
| r(C2,4-H) Å || 1.0835
|-
| r(C3-H) Å || 1.0852
|-
| r(N-C1,5) Å || 1.3524
|-
| r(C1,5-C2,4) Å || 1.3839
|-
| r(C2,4-C3) Å || 1.3988
|-
| θ(C2-C3-C4) degrees(º) || 120
|-
| θ(C3-C2,4-C1,5) degrees(º) || 119
|-
| θ(C2,4-C1,5-B) degrees(º) || 119
|-
| θ(C1,5-N-C5,1) degrees(º) || 123
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Pyridinium ====

Frequency calculation for Pyridinium can be found [[Media:JL PYRIDINIUM FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -9.6416 -5.4848 -0.0009 -0.0009 -0.0005 3.5883
Low frequencies --- 391.8846 404.3533 620.1926
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|392
|1
|Very Slight
|Bend
|-
|404
|0
|No
|Bend
|-
|620
|0
|No
|Bend
|-
|645
|0
|No
|Bend
|-
|677
|90
|Yes
|Bend
|-
|748
|3
|Yes
|Bend
|-
|854
|11
|Yes
|Bend
|-
|883
|0
|No
|Bend
|-
|992
|2
|Slight
|Bend
|-
|1006
|0
|No
|Bend
|-
|1022
|4
|Yes
|Stretch
|-
|1048
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1082
|3
|Yes
|Stretch
|-
|1087
|4
|Yes
|Stretch
|-
|1200
|3
|Yes
|Bend
|-
|1229
|2
|Slight
|Bend
|-
|1300
|3
|Yes
|Stretch
|-
|1374
|11
|Yes
|Stretch
|-
|1416
|3
|Yes
|Stretch
|-
|1524
|21
|Yes
|Stretch
|-
|1580
|48
|Yes
|Stretch
|-
|1657
|32
|Yes
|Stretch
|-
|1676
|34
|Yes
|Stretch
|-
|3224
|0
|No
|Stretch
|-
|3240
|1
|Slight
|Stretch
|-
|3242
|11
|Yes
|Stretch
|-
|3252
|20
|Yes
|Stretch
|-
|3254
|0
|No
|Stretch
|-
|3569
|158
|Yes
|Stretch
|}

[[File:JL Pyridinium frequency Spectrum.PNG|thumb|center|IR Spectrum of Pyridinium|400px]]

==== Molecular Orbital Analysis for Boratabenzene ====
{{DOI|10042/195351}}

==== NBO Analysis for Boratabenzene ====
{{DOI|10042/195351}}

[[File:JL Pyridinium NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Pyridinium.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.483
|-
| H(-C1,5) || 0.285
|-
| H(-C2,4) || 0.297
|-
| H(-C3) || 0.292
|-
| C1,5 || 0.071
|-
| C2,4 || -0.241
|-
| C3 || -0.122
|-
| B || -0.476
|}

=== Borazine ===

==== Optimisation of Borazine ====
Optimisation file of Borazine with 6-31G (d,p) basis set can be found [[Media:JL_BORAZINE_OPT.LOG| here]].

{| class="wikitable" border="1"
|+ Optimised Borazine Summary Table
! Summary Data !! Convergence !! Jmol
|-
| [[File:JL Borazine Opt ResultsSummary.PNG|300px]]
| [[File:JL Borazine Opt Congerence.PNG]]
| <jmol><jmolApplet>
<title> Borazine Optimised 6-31G (d,p)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>JL Borazine Opt.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

==== Geometry Data ====

{| class="wikitable"
|+ Geometry Data
! !! NH3BH3
|-
| r(N-H) Å || 1.0098
|-
| r(B-H) Å || 1.1949
|-
| r(B-N) Å || 1.4307
|-
| θ(B-N-B) degrees(º) || 123
|-
| θ(N-B-N) degrees(º) || 117
|-
| θ(H-C/H-N) degrees(º) || 180
|}

==== Frequency Analysis for Borazine ====

Frequency calculation for Borazine can be found [[Media:JL_BORAZINE_FREQUENCY.LOG| here]].

{| class="wikitable"
|+
! Summary Data !! Low Modes
|-

|[[File:JL_Pyridinium_Frequency_ResultsSummary.PNG|300px]]
|
<pre>
Low frequencies --- -0.0286 -0.0125 -0.0041 2.9117 2.9386 4.0716
Low frequencies --- 289.7147 289.7154 404.4139
</pre>
|}

{| class="wikitable"
|+
|-
|Wavenumber || Intensity || IR active? ||Type
|-
|290
|0
|No
|Bend
|-
|290
|0
|No
|Bend
|-
|404
|24
|Yes
|Bend
|-
|525
|1
|Slight
|Bend
|-
|525
|1
|Slight
|Bend
|-
|710
|0
|No
|Bend
|-
|710
|0
|No
|Bend
|-
|732
|60
|Yes
|Bend
|-
|864
|0
|No
|Stretch
|-
|928
|0
|No
|Bend
|-
|928
|0
|No
|Bend
|-
|937
|236
|Yes
|Bend
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|945
|0
|No
|Stretch
|-
|1052
|0
|No
|Bend
|-
|1081
|0
|No
|Stretch
|-
|1081
|0
|No
|Stretch
|-
|1245
|0
|Yes
|Stretch
|-
|1314
|0
|No
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1400
|11
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|1492
|494
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2641
|284
|Yes
|Stretch
|-
|2651
|0
|No
|Stretch
|-
|3642
|0
|No
|Stretch
|-
|3643
|40
|Yes
|Stretch
|-
|3643
|40
|Yes
|Stretch
|}

[[File:JL Borazine frequency Spectrum.PNG|thumb|center|IR Spectrum of Borazine|400px]]

==== Molecular Orbital Analysis for Borazine ====
{{DOI|10042/195353}}

==== NBO Analysis for Borazine ====
{{DOI|10042/195353}}

[[File:JL Borazine NBOAnalysis.PNG|thumb|center|Charge distribution of the NBOs of Borazine.|400px]]

{| class="wikitable" border="1"
|+
! '''Atom''' !! '''Charge'''
|-
| H(-N) || 0.432
|-
| H(-B) || -0.077
|-
| N || -1.102
|-
| B || 0.747
|}

==MO Comparison==

===Comparison 1===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:Benzene MO(7) 1.PNG|250px]]
| [[File:Boratabenzene MO(7) 1.PNG|250px]]
| [[File:Pyridinium MO(7) 1.PNG|250px]]
| [[File:Borazine MO(7) 1.PNG|250px]]
|-
| Energy / au
| -0.74000
| -0.51956
| -0.99321
| -0.83516
|-
| Order
| 9th
| 8th
| 9th
| 8th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

===Comparison 2===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:NM Benzene comp 2 MO.jpg|250px]]
| [[File:NM Boratabenzene comp 2 MO.jpg|250px]]
| [[File:NM Pyridium comp 2 MO.jpg|250px]]
| [[File:NM Borazine comp 2 MO.jpg|250px]]
|-
| Energy / au
| -0.41653
| -0.20373
| -0.65086
| -0.43403
|-
| Order
| 15th
| 14th
| 16th
| 13th
|-
| Degenerate?
| Yes
| No
| No
| Yes
|}

===Comparison 3===

{| class="wikitable"
!
! Benzene
! Boratabenzene
! Pyridinium
! Borazine
|-
| MO
| [[File:NM Benzene comp 3 MO.jpg|250px]]
| [[File:NM Boratabenzene comp 3 MO.jpg|250px]]
| [[File:NM Pyridium comp 3 MO.jpg|250px]]
| [[File:NM Borazine comp 3 MO.jpg|250px]]
|-
| Energy / au
| -0.35994
| -0.13209
| -0.64062
| -0.36134
|-
| Order
| 17th
| 17th
| 17th
| 17th
|-
| Degenerate?
| No
| No
| No
| No
|}

This molecular orbital shows the delocalised π system,. It constitutes entirely of px orbitals found above and below the plane of the ring giving in phase strong through space bonding with no anti bonding component present.

The calculated MOs for all four molecules show a very similar shape with the only differences being a bulging of the orbital around the respective electronegative parts of the molecule: the carbon in the four position in boratabenzene and the nitrogen atoms found in pyridinium and borazine. This is to be expected as more electronegative atoms draw electron density closer to themselves.

The relative energies of the orbitals can be explained in a similar fashion to the orbitals in Comparison 2 in that boron and nitrogen destabilise and stabilise respectively and the symmetry of the borazine atom allows for balance between these effects.

The orbitals all have the same order (17th) which is due to this orbital's contribution to the aromaticity of the molecule which is why there are also no degenerate orbitals present in each molecule.

Where the LCAO suffers in its predictive ability is that it is unable to determine how much each atom's px orbital will contribute to the overall molecular orbital, however knowledge of electronegativities does make this possible to predict without the use of LCAO. All in all, this is a further demonstration of why it is important to calculate the MOs rather than relying on LCAO theory.

===Effects of substituition===

Any form of alteration of the structure of the benzene molecule leads to a change in the MO. Not only due to there being different atoms present but also affecting the symmetry of the molecule and so its point group allocation.

{| class="wikitable"
! Molecule
! Point Group
|-
| Benzene || D6h
|-
| Boratabenzene || C2v
|-
| Pyridinium || C2v
|-
| Borazine || D3h
|}

As seen above, the molecules all have a different point group from benzene which means the MOs formed will also have different symmetry labels and so will also have different structures as seen in the comparisons above.

The effect of changing a single atom in the case of boratabenzene and pyridinium means the molecule is not made entirely of a repeat unit, the eigenvalues of the orbitals change, likewise the relative energies, in such a manner that no two orbitals are degenerate. The borazine molecule is however made up of a repeat unit and so it is possible to form degenerate orbitals, as seen in the list of MOs below.

The stability of the molecule is also dependent on the atoms present. As the table below shows, pyridinium is the most stable aromatic compound, followed by borazine, benzene and finally boratabenzene which in it's aromatic form is slightly unstable. Benzene and borazine are fairly similar in their MO structure and energies (HOMOs at -0.24690 and -0.27593) which can be explained by the presence of repeat units throughout the compounds allowing for a more equal distribution of electron density. Borazine lies slightly lower in energy due to the presence of nitrogen atoms, which due to their strong electronegativity are able to hold electron density closer than the boron's slight electropositivity. The overall balance between the nitrogen and boron's electronegativities is a more stabilising effect than benzene's uniform carbon ring.

Pyridinium is the most stable molecule with its HOMO at -0.47886. The nitrogen's strong electronegativity is responsible for this value as this atom is able to draw the 6 π electron density closer towards itself and keep the molecule as a whole more stable. Even though there is a significant energy jump to its LUMO (-0.25841), this still lies lower than benzene's HOMO and means that the orbital is harder to access and so harder to be attacked by an electrophile.

Boratabenzene is the most unstable molecule with its HOMO at 0.01095 and its LUMO at 0.21473 making it a quite accessible orbital to undergo electrophilic attack. The reason why the molecule is unstable is due to the boron atom being present. Boron is an electropositive atom and so diverts electron density away from itself. The other atoms in the ring are carbon atoms and they aren't electronegative enough to stabilise the 6 delocalised π electrons well enough and so the stability of the molecule decreases.

File:Pyridinium MO(7) 1.PNG

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File:Borazine MO(7) 1.PNG

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File:Boratabenzene MO(7) 1.PNG

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File:Benzene MO(7) 1.PNG

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