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Rep:Mod:XYZ12384

2013-11-22T18:25:52Z

Sjp211: /* Spectroscopy of an intermediate related to the synthesis of Taxol */

=='''EXPERIMENT 1C'''==
''Part 1''

==='''The Hydrogenation of Cyclopentadiene Dimer'''===

2 molecules of cyclopentadiene can react by a Diels-Alder reaction to give dicyclopentadiene. I drew molecules 1 to 4 with ChemBio3D and then opened them in Avogadro where I minimised their geometry and hence obtained a value for their energy.

[[Image:1CSet.jpg|500px|right|frame|Molecules 1-4]]
[[Image:Endoexocp.jpg|500px|right|frame|Endo and exo]]

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecule'''
| width="150" | '''Model'''

|- align="center"
| ''Dimer 1 (exo)''
|
<jmol><jmolApplet><title>Alkene2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Thurs1.cml</uploadedFileContents>
</jmolApplet></jmol>
|- align="center"
| ''Dimer 1 (endo)''
|
<jmol><jmolApplet><title>Alkene2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Thurs2.cml</uploadedFileContents>
</jmolApplet></jmol>
|- align="center"
| ''Dihydro derivative 3
|
<jmol><jmolApplet><title>Alkene2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Thurs3.cml</uploadedFileContents>
</jmolApplet></jmol>
|- align="center"
| ''Dihydro derivative 4''
|
<jmol><jmolApplet><title>Alkene2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Thurs4.cml</uploadedFileContents>
</jmolApplet></jmol>
|}

{| border
|
|'''Dimer 1'''
|'''Dimer 2'''
|'''Dihydro derivative 3'''
|'''Dihydro derivative 4'''
|----
|'''Energy (kcal/mol)'''
| 55.46794
| 58.19067
| 50.44566
| 41.25749
|----
|
|
|
|
|
|----
|'''Total bond stretching energy (kcal/mol)'''
| 3.54301
| 3.46794
| 3.31218
| 2.82311
|----
|'''Total angle bending energy (kcal/mol)'''
|30.77268
|33.18929
|31.93090
|24.68536
|----
|'''Total stretch bending energy (kcal/mol)'''
| -2.04139
| -2.08220
| -2.10228
| -1.65719
|----
|'''Total torsional energy (kcal/mol)'''
| -2.73103
| -2.94947
| -1.46634
| -0.37840
|----
|'''Total out of plane bending energy (kcal/mol)'''
| 0.01485
| 0.02182
| 0.01310
| 0.00028
|----
|'''Total van der Waals energy (kcal/mol)'''
| 12.80164
| 12.35875
| 13.63862
| 10.63731
|----
|'''Total electrostatic energy (kcal/mol)'''
| 13.01367
| 14.18454
| 5.11949
| 5.14702
|----
|}

It is known that cyclopentadiene dimerises to produce specifically the endo dimer 2 rather than the exo dimer 1. The endo dimer is that with the substituents directed towards each other, whereas the exo dimer is that with the substituents away from each other. As calculated, the endo dimer is of higher energy than the exo dimer - 58kcal/mol compared to 55kcal/mol; it is reasonable to think that it would be less stable for steric reasons; so why is it the favoured product? Theories behind why are numerous, mainly involving the favourable orbital overlap in the transition state, so called secondary orbital interactions. The endo dimer is therefore the kinetic product i.e. the product formed first, although not the thermodynamically most stable, and will be formed preferentially (providing the reaction time is not overly long and the reaction temperature is not overly high).

Regarding the dihydro derivatives, derivative 4 is of lower energy than derivative 3, and is therefore more thermodynamically stable. This means that breaking the double bond in the 6-membered ring would be a reaction under thermodynamic control, whereas if the double bond in the 5-membered ring were to be broken this would be under kinetic control.
Identifying why derivative 4 is more stable than derivative 3 is needed. Derivative 3 has a larger Van der Waals energy, presumably because with the double bond in the 5 membered ring, there are more steric interactions between neighbouring groups, here unfavourable. Although the derivative 3 actually has more stable torsional energy and stretch bending, it has significantly higher angle bending energy.
Calculating the energy for the dihydro derivatives involved some manual manipulation of the optimised structures, especially to ensure that the labelled hydrogen atoms remained in the position that they have in the diagram.

==='''Atropisomerism in an Intermediate related to the Synthesis of Taxol.'''===

Below are pictured two atropisomers of an intermediate in the synthesis of Taxol, which differ only in whether the C=O bond points upwards or downwards. Having drawn them both in ChemBio3D, I proceeded to minimise their geometry in Avogadro to determine which is the most stable. This required much manual manipulation of the geometry to ensure that the rings displayed the correct conformation, in particular.

[[Image:Thurs910.jpg|500px|right|frame|Intermediates 9 and 10]]

{|border
|
|'''Intermediate 9'''
|'''Intermediate 10'''
|----
|'''Energy (kcal/mol)'''
|121.81932
|126.32222
|----
|
|
|
|----
|'''Total bond stretching energy (kcal/mol)'''
|12.98361
|14.85958
|----
|'''Total angle bending energy (kcal/mol)'''
|50.10469
|48.00565
|----
|'''Total stretch bending energy (kcal/mol)'''
| -0.49774
| -0.60146
|----
|'''Total torsional energy (kcal/mol)'''
|8.17105
|8.49999
|----
|'''Total out of plane bending energy (kcal/mol)'''
|2.63558
|2.60344
|----
|'''Total van der Waals energy (kcal/mol)'''
|46.85942
|51.07448
|----
|'''Total electrostatic energy (kcal/mol)'''
|1.56271
|1.88054
|----
|}

From this initial energy determination, it is apparent that intermediate 9 is of slightly lower energy than intermediate 10, however this difference is quite slight, and could have been reversed, depending on the quantity and quality of the optimisations. Although I went through several stages of optimising the structures, it was difficult to obtain more than slight decreases in energy each time. In theory, intermediate 9 should have its C ring in a twist boat form, which I think I achieved, with that for intermediate 10 in a chair form, which was harder to keep.

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecule'''
| width="150" | '''Model'''

|- align="center"
| ''Intermediate 9''
|
<jmol><jmolApplet><title>Alkene2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Thurs9.cml</uploadedFileContents>
</jmolApplet></jmol>
|- align="center"
| ''Intermediate 10''
|
<jmol><jmolApplet><title>Alkene2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Thurs10.cml</uploadedFileContents>
</jmolApplet></jmol>
|}

'''Hyperstable alkenes'''

Alkenes such as this are described as 'hyperstable'. This is because of their position at a bridgehead which stabilises the alkene. Of course an alkene in such a ring has a degree of strain; yet the alkene has reduced strain compared to its corresponding alkane and hence the hydrogenation enthalpy for such alkenes is less than for more typical alkenes, removing the thermodynamic driving force for the reaction. The presence of the methyl groups on the bridge reinforces this effect; it would indeed be even more pronounced with more sterically demanding groups.

===Spectroscopy of an intermediate related to the synthesis of Taxol===

Derivatives of intermediates 9 and 10, so-called intermediates 17 and 18, are pictured here. It was my job to calculate both 1H and 13C NMR spectra for these molecules, after first optimising their geometry, as above.

[[Image:TAXOL17-18forWiki.jpg|400px|left|frame|Taxol intermediates 17 and 18]]

'''Taxol intermediate 18'''

''Spectra''

[[File:TAXOLNMR13CforWiki.svg|400px|left|thumb|13C NMR of Taxol intermediate 18]]

[[File:TAXOLNMR1HforWiki.svg|400px|centre|thumb|1H NMR of Taxol intermediate 18]]

{{DOI|10042/25972}}

''Data''

''13C''

{| border
|
|'''Chemical shift (ppm) (x-axis)'''
|'''Intensit (y-axis)'''
|'''Degeneracy'''
|'''Literature value of chemical shift (ppm)'''
|'''Chemical shift percentage difference (%)'''
|----
|'''14-C'''
|218.7122426
|1
|1
|211.49
|3.42
|----
|'''3-C'''
|145.566623
|1
|1
|148.72
|2.12
|----
|'''6-C'''
|122.1221296
|1
|1
|120.90
|1.01
|----
|'''9-C'''
|90.25778571
|1
|1
|74.61
|21.0
|----
|'''13-C'''
|57.57937432
|1
|1
|60.53
|4.87
|----
|'''8-C'''
|56.98823281
|1
|1
|51.30
|11.1
|----
|'''4-C'''
|53.93147108
|1
|1
|50.94
|5.87
|----
|'''16-C'''
|51.45746873
|1
|1
|45.53
|13.0
|----
|'''10-C'''
|50.32133636
|1
|1
|43.28
|16.3
|----
|'''22-C'''
|47.94804848
|1
|1
|40.82
|17.5
|----
|'''5-C'''
|47.62182749
|1
|1
|38.73
|23.0
|----
|'''21-C'''
|42.12141597
|1
|1
|36.78
|14.5
|----
|'''12-C'''
|42.00330074
|1
|1
|35.47
|18.4
|----
|'''7-C'''
|30.87297377
|1
|1
|30.84
|0.107
|----
|'''2-C'''
|30.5765739
|1
|1
|30.00
|1.92
|----
|'''1-C'''
|27.36074611
|1
|1
|25.56
|7.05
|----
|'''17-C'''
|26.48312723
|1
|1
|25.35
|4.47
|----
|'''11-C'''
|22.50667999
|1
|1
|22.21
|1.34
|----
|'''18-C'''
|19.71519254
|1
|1
|21.39
|7.83
|----
|'''19-C'''
|17.49142381
|1
|1
|19.83
|11.8
|----
|}

Reference: TMS B3LYP/6-31G(d,p) chloroform; Reference shielding: 192.17 ppm; NMR Degeneracy Tolerance: 0.05

''1H''

{| border
|
|'''Chemical shift (ppm) (x-axis)'''
|'''Intensity (y-axis)'''
|'''Degeneracy'''
|'''Literature value of chemical shift (ppm)'''
|----
|31-H
|5.033281522
|1
|1
|5.21
|----
|53-H
|3.287281382
|1
|1
|3-2.7
|----
|52-H
|3.171685827
|1
|2
|----
|50-H
|3.162427902
|2
|2
|----
|34-H
|3.031182432
|1
|2
|----
|51-H
|3.025883691
|2
|1
|----
|32-H
|2.929098468
|1
|1
|----
|25-H
|2.702363379
|1
|1
|2.7-2.35
|----
|33-H
|2.639715167
|1
|1
|----
|29-H
|2.510863665
|1
|3
|----
|30-H
|2.474489955
|2
|3
|----
|44-H
|2.467717465
|3
|3
|2.2-1.7
|----
|36-H
|2.321118582
|1
|4
|----
|24-H
|2.28204336
|2
|4
|----
|35-H
|2.24094819
|3
|4
|----
|27-H
|2.232855901
|4
|4
|----
|28-H
|2.125579451
|1
|1
|----
|26-H
|1.708709036
|1
|3
|1.58
|----
|38-H
|1.672449177
|2
|3
|1.5-1.2
|----
|48-H
|1.64327592
|3
|3
|----
|39-H
|1.520852921
|1
|2
|----
|41-H
|1.511494528
|2
|2
|1.1
|----
|37-H
|1.416837673
|1
|3
|----
|47-H
|1.402531022
|2
|3
|----
|40-H
|1.365898688
|3
|3
|1.07
|----
|49-H
|1.0293207
|1
|1
|----
|46-H
|0.905573979
|1
|4
|----
|42-H
|0.884744233
|2
|4
|1.03
|----
|43-H
|0.857346606
|3
|4
|----
|45-H
|0.843911059
|4
|4
|----
|}

Reference: TMS B3LYP/6-31G(d,p) chloroform; Reference shielding: 31.7462 ppm; NMR Degeneracy Tolerance: 0.05

It is a little harder to directly compare the calculated NMR data with that from literature for 1H NMR due to the presence of multiplets. An important piece of information that is missing from the calculated data is the coupling constants, but this takes a lot of computation time.

Some assignments can be made for specific H atoms. The alkene proton (A) is likely to be at 5.1ppm, with the four sulphide protons (C) at 2.7-2.35ppm. The B protons could be at 3-2.7ppm. D at 2.2-1.7ppm; E at 1.58ppm;

[[Image:TAXOL18assigned.jpg|500px|left|frame|Taxol intermediate 18 1H NMR: assigned]]

'''Taxol Intermediate 17'''

''Spectra''

[[File:TAXOL1713CNMRforWiki.svg|400px|left|thumb|13C NMR of Taxol intermediate 17]]

[[File:TAXOL171HNMRforWiki.svg|400px|centre|thumb|1H NMR of Taxol intermediate 17]]

{{DOI|10042/25975}}

''Data''

''13C''

{| border
|
|'''Chemical shift (ppm) (x-axis)'''
|'''Intensity (y-axis)'''
|'''Degeneracy'''
|'''Literature value of chemical shift (ppm)'''
|'''Chemical shift percentage difference(%)'''
|----
|'''9-C'''
|217.61
|1
|1
|218.79
|0.54
|----
|'''5-C'''
|159.17
|1
|1
|144.63
|10.1
|----
|'''15-C'''
|121.60
|1
|1
|125.33
|2.98
|----
|'''7-C'''
|94.23
|1
|1
|72.88
|29.3
|----
|'''8-C'''
|62.56
|1
|1
|56.19
|11.3
|----
|'''10-C'''
|60.09
|1
|1
|52.52
|14.4
|----
|'''20-C'''
|47.39
|1
|1
|48.50
|2.47
|----
|'''4-C'''
|44.95
|1
|1
|46.80
|3.95
|----
|'''21-C'''
|43.05
|1
|1
|45.76
|5.92
|----
|'''23-C'''
|42.85
|1
|1
|39.80
|7.67
|----
|'''6-C'''
|42.01
|1
|1
|38.81
|8.25
|----
|'''2-C'''
|40.84
|1
|1
|25.85
|13.9
|----
|'''18-C'''
|37.12
|1
|1
|32.66
|13.7
|----
|'''16-C'''
|33.38
|1
|1
|28.79
|15.9
|----
|'''1-C'''
|33.33
|1
|1
|28.29
|17.8
|----
|'''17-C'''
|30.43
|1
|1
|26.88
|13.2
|----
|'''11-C'''
|22.75
|1
|1
|25.66
|11.3
|----
|'''12-C'''
|22.46
|1
|1
|23.86
|5.87
|----
|'''14-C'''
|22.28
|1
|1
|20.96
|6.30
|----
|'''19-C'''
|21.72
|1
|1
|18.71
|16.1
|----
|}

Reference: TMS B3LYP/6-31G(d,p) chloroform; Reference shielding: 192.17 ppm; NMR Degeneracy Tolerance: 0.05

''1H''

{|border
|
|'''Chemical shift (ppm) (x-axis)'''
|'''Intensity (y-axis)'''
|'''Degeneracy'''
|'''Literature value of chemical shift (ppm)'''
|----
|29-H
|5.50
|1
|1
|4.84
|----
|28-H
|3.65
|1
|1
|3.4-3.10
|----
|32-H
|3.27
|1
|4
|----
|49-H
|3.23
|2
|4
|----
|48-H
|3.23
|3
|4
|----
|51-H
|3.22
|4
|4
|2.99
|----
|50-H
|3.04
|1
|1
|2.80-1.35
|----
|30-H
|2.92
|1
|2
|----
|52-H
|2.91
|2
|2
|----
|26-H
|2.82
|1
|1
|----
|47-H
|2.73
|1
|1
|----
|53-H
|2.33
|1
|2
|----
|43-H
|2.28
|2
|2
|----
|27-H
|2.09
|1
|3
|----
|42-H
|2.07
|2
|3
|----
|25-H
|2.07
|3
|3
|----
|31-H
|2.00
|1
|1
|----
|44-H
|1.81
|1
|2
|----
|35-H
|1.78
|2
|2
|----
|45-H
|1.72
|1
|1
|----
|24-H
|1.64
|1
|2
|1.38
|----
|39-H
|1.62
|2
|2
|----
|41-H
|1.48
|1
|2
|----
|36-H
|1.48
|2
|2
|1.25
|----
|40-H
|1.25
|1
|2
|----
|46-H
|1.20
|2
|2
|----
|33-H
|0.98
|1
|1
|1.10
|----
|34-H
|0.87
|1
|1
|----
|38-H
|0.82
|1
|1
|----
|37-H
|0.71
|1
|1
|1.00-0.80
|----
|}

Reference: TMS B3LYP/6-31G(d,p) chloroform; Reference shielding: 31.7462 ppm; NMR Degeneracy Tolerance: 0.05

Further optimisation of the structures would have led to NMR spectra that are closer to those of the literature. All NMR data for intermediates 17 and 18 originates from the same source.<ref>L. A. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, Journal of the American Chemical Society, 1990, '''112''', 277-283.</ref> Although there is a degree of similarity between the calculated and literature data - they are at least recognisable and vaguely diagnostic of a particular molecule - some of the percentage differences are very large. It is possible that literature values could be incorrect; in this case I believe it is my unskilled ability in optimising the structures of the molecules that is mainly responsible for the differences.

In addition to calculating NMR spectra, it was possible to obtain values for the free energies of the two intermediates. This is given by the 'Sum of electronic and thermal free energies' in the output file.

'''Sum of electronic and thermal free energies''' = -1651.469051, for intermediate 18

'''Sum of electronic and thermal free energies''' = -1651.38004, for intermediate 17

This shows that intermediate 18, with the 'tucked under' C=O is of slightly lower energy than intermediate 17. This confirms that the direction of the arrow in the above image is correct (or at least a version of the true equilibrium). Intermediate 18 has a structure that minimises steric interactions between non-bonded groups.<ref>L. A. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, Journal of the American Chemical Society, 1990, 112, 277-283</ref>

''Part 2''

==='''Analysis of the properties of the synthesised alkene epoxides'''===

Whilst in the lab during Experiment 1S, in pairs we synthesised both Jacobsen and Shi catalysts. Once given a set of 4 alkenes -
styrene, β-methyl styrene, trans-stilbene and 1,2-dihydronaphthalene - we proceeded to carry out asymmetric epoxidation of these alkenes using the aforementioned catalysts. Reproduced here are the structures of stable pre-catalysts 21 and 23.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| ''Pre-catalyst 21''
|
[[Image:Precatalyst21.jpg|150px]]
|- align="center"
| ''Pre-catalyst 23''
|
[[Image:Precatlyst23.jpg|150px]]
|}

====The crystal structures of the two catalysts====

[[Image:precatalyst23mercury.jpg|200px|centre|frame|Pre-catalyst 21]]

[[Image:precatalyst21lengths.jpg|200px|centre|thumb|Pre-catalyst 21]]

I searched for the structure of pre-catalyst 21 on the Cambridge Crystal Database. Its reference is NELQEA01. I
measured the 2 C-O bond lengths for each anomeric centre. As shown in the diagram, the sets of C-O lengths are:
1.456/1.428 and 1.454/1.423; 1.442/1.430 and 1.460/1.406. What is surprising is that for each anomeric centre, the two
C-O bond lengths are not of the same length; in fact there is a definite longer and shorter bond although both are typical of such a C-O bond (with some variation between the actual lengths for each anomeric centre). This must mean that one of the C-O bonds has more double bond character than the other. The 6 membered ring can be drawn in a chair form as below (additional substituents have been discarded). This puts one of the C-O bonds for each anomeric centre axial and one equatorial. Possible reactions include elimination of a H anti-periplanar to a C-O leading to formation of an alkene and O-, or equivalent with the O lone pair.

[[Image:chairform2.jpg|200px|left|frame|Partial chair form of pre-catalyst 21]]

I also looked for the crystal structure of pre-catalyst 23 on the Cambridge Crystal Database.
The reference is TUVNIB01. As shown on the diagram, the closest approach between adjacent t-Bu groups on the rings (H-H)
was found to be 2.081. This is surprisingly close, especially considering that the closest approach for two t-Bu groups
on the ring was found to be 3.602 or 3.557 for each ring.

[[Image:precatalyst23lengths.jpg|200px|right|thumb|Pre-catalyst 23]]

====The calculated NMR properties of your products====

I calculated both 1H and 13C NMR spectra for the epoxides of both trans-stilbene and 1,2-dihydro naphthalene, with undefined stereochemistry. These are a complementary pair to use, as trans-stilbene is a trans alkene and
1,2-dihydro naphthalene is a cis alkene.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''NMR spectrum'''
| width="150" | '''DOI'''

|- align="center"
| ''Epoxide of trans-stilbene: 13C''
|
[[File:trans-stilbene.epoxideCNMRforWiki.svg|150px]]
|{{DOI|10042/25974}}
|- align="center"
| ''Epoxide of trans-stilbene: 1H''
|
[[File:trans-stilbene.epoxideHNMRforWiki.svg|150px]]
|{{DOI|10042/25974}}
|- align="center"
| ''Epoxide of 1,2-dihydronaphthalene: 13C''
|
[[File:napht.epoxideCNMRforWiki.svg|150px]]
|{{DOI|10042/25973}}
|- align="center"
| ''Epoxide of 1,2-dihydronaphthalene: 1H''
|
[[File:napht.epoxideHNMRforWiki.svg|150px]]
|{{DOI|10042/25973}}
|}

[[Image:trans-stilbene.epoxide.jpg|200px|left|frame|Epoxide of trans-stilbene (no stereochemistry)]]
[[Image:napht.epoxide.jpg|200px|left|frame|Epoxide of 1,2-dihydro naphthalene (no stereochemistry)]]

Reference NMR data for epoxide of trans-stilbene:
'''1H NMR''' (300MHz, CDCl3) Chemical shift (ppm): 3.86 (s,2H), 7.26-7.45 (m,10H)
The calculated values are 3.54, 7.45-7.57, which is a fairly good match.

'''13C NMR''' (75MHz, CDCl3) Chemical shift (ppm): 62.81, 125.4, 128.19, 128.44, 136.99.
The calculated values are 66.43, 118.27, 123.08, 123.21, 123.52, 124.22, 134.08. Although these figures do not exactly match, and there is overlap within the sets, taking each shift to be related to its partner compares well (i.e. good percentage difference.)

<ref>R. W. Murray, M. Singh, Organic Syntheses Coll., 1998, '''9''', 288</ref>

Reference NMR data for epoxide of 1,2-dihydronaphthalene:
'''1H NMR''' (CDCl3) Chemical shift (ppm): 1.65 (m,1H), 2.30 (m,1H), 2.44(m,1H), 2.68(m,1H), 3.62 (m,1H), 3.74 (d,J=4,1H), 6.98 (d,J=7, 1H), 7.08-7.17 (m,2H), 7.28 (d,J=8,1H).
The calculated values are 1.87, 2.21, 2.27, 2.95, 3.48, 3.55, 7.25, 7.39, 7.61. These values are less of a good match, probably suggesting that the structure of the rings needed further optimisation.

'''13C NMR''' (CDCl3) Chemical shift (ppm): 21.8,24.4,52.7,55.1,126.1,2x128.4,129.5,132.6,136.7.
The calculated values are 29.1, 30.2, 52.1, 52.8, 121.7, 123.5, 123.8, 126.7, 130.4, 135.4. Although the match improves (and any difference becomes less significant) for the higher chemical shift values, there is a fairly large mismatch for the lower chemical shifts.

<ref>K. Smith, C-H. Liu, G. A. El-Hiti, Organic and Biomolecular Chemistry, 2006, '''4''', #5, 917-927</ref>

In conclusion, the literature values tend to support those that which were calculated, with some variation.

====Assigning the absolute configuration of the product====
'''The reported literature for optical rotations and the calculated chiroptical properties of the products'''

I looked on Reaxys for optical rotatory power literature values for each epoxide - both isomers - of the four alkenes. I also calculated values for one of the two isomers (assuming that calculation of the other isomer would return a result equal in magnitude but opposite in sign). Although I did not fully optimise the structures, and hence the obtained values do not match the literature values at all well in magnitude, the main purpose of this search is to check that the values have the correct sign of rotation. The magnitude of optical rotation values on Reaxys varies a lot; as well as the sign of the optical rotation, particularly for styrene oxide.

(R,R) epoxide of trans-stilbene: '''310 deg'''
<ref>R. I. Kureshy, S. Singh, N. H. Khan, S. H. R. Abdi, S. Agrwawal, R. V. Jasra, Tetrahedron: Assymetry, 2006, '''17''', #11, 1638-1643</ref>;
(S,S) epoxide of trans-stilbene: '''-313 deg'''
<ref>Read, Campbell, Nature, 1930, '''125''', 16</ref>

I calculated an optical rotation for the (R,R) epoxide of trans-stilbene as '''30.74 deg'''. {{DOI|10042/26005}}

(S,S) epoxide of β-methyl styrene: '''-41.8 deg'''.
<ref>H. Lin, Y. Liu, Z-L. Wu, Tetrahedron: Assymetry, 2011, '''22''', #2, 134-137</ref>;
(R,R) epoxide of β-methyl styrene: '''40.8 deg'''.
<ref>B. Wang, X-Y. Wu, O. A. Wong, B. Nettles, M-X Zhao, D. Chen, Shi, Yian, Journal of Organic Chemistry, 2009, '''74''', #10, 3986-3989</ref>

I calculated an optical rotation for the (S,S) epoxide of β-methyl styrene as '''-118.47 deg'''. {{DOI|10042/26004}}

(S) epoxide of styrene: '''-44.5 deg'''.
<ref>B. T. Cho, W. K. Yang, O.K. Choi, Journal of the Chemical Society, Perkin Transactions 1, 2001 , #10, 1204-1211</ref>;
(R) epoxide of styrene: '''42.7 deg'''.
<ref>E. J. Corey, C. J. Helal, Tetrahedron Letters, 1993, '''34''', # 33, 5227-5230</ref>

I calculated an optical rotation for the(R) epoxide of styrene as '''180.06 deg''' ({{DOI|10042/26001}}) and for the (S) epoxide of styrene as '''-182.37 deg''' ({{DOI|10042/26002}}) (very almost equal and opposite.)

(1S,2R) epoxide of 1,2-dihydronaphthalene: '''-134.5 deg'''.
<ref>A. Shcmid, K. Hofstetter, H-J. Feiten, F. Hollmann, B. Witholt, Advanced Synthesis and Catalysis, 2001, '''343''', #6-7, 732-737</ref>;
(1R,2S) epoxide of 1,2-dihydronaphthalene: '''133 deg'''.
<ref>D. R. Boyd, N. D. Sharma, R. Agarwal, N. A. Kerley, R. A. S. McMordie, et al, Journal of the Chemical Society Chemical communications, 1994, #14, 1693-1694</ref>

I calculated an optical rotation for the (1R,2S) epoxide of 1,2-dihydronaphthalene as '''52.74 deg'''. {{DOI|10042/26003}}

In conclusion, the calculated optical rotations indicate that the literature references included are correct. However, it was the case that some of the literature assignments had signs for the optical rotation which were incorrect. Images of each isomer are included below for clarity.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| ''(R,R) epoxide of trans-stilbene''
|
[[Image:(R,R)stilbeneepoxide.jpg|150px]]
|- align="center"
| ''(S,S) epoxide of trans-stilbene''
|
[[Image:(S,S))stilbeneepoxide.jpg|150px]]
|- align="center"
| ''(R,R) epoxide of β-methyl styrene''
|
[[Image:(R,R)methylstyreneepoxide.jpg|150px]]
|- align="center"
| ''(S,S) epoxide of β-methyl styrene''
|
[[Image:(S,S)methylstyreneepoxide.jpg|150px]]
|- align="center"
| ''(R) epoxide of styrene''
|
[[Image:Rstyreneepoxide.jpg|150px]]
|- align="center"
| ''(S) epoxide of styrene''
|
[[Image:(S)styreneepoxide.jpg|150px]]
|- align="center"
| ''(1R,2S) epoxide of 1,2-dihydronaphthalene''
|
[[Image:(1R,2S)naphtepoxide.jpg|150px]]
|- align="center"
| ''(1S,2R) epoxide of 1,2-dihydronaphthalene''
|
[[Image:(1S,2R)naphtepoxide.jpg|150px]]
|}

I additionally calculated VCD (vibrational circular dichroism) spectra for one of the two isomers of each epoxide (the same isomers that were used for calculation of optical rotation for comparison; again with both (R) and (S) epoxides of styrene as a check). Although I attempted to create ECD (electronic circular dichroism) spectra as well, I ought to have heeded the advice that this wasn't appropriate in this case because these epoxides lack an appropriate chromophore.

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Molecule'''
| width="150" | '''VCD spectrum'''
| width="150" | '''DOI'''

|- align="center"
| ''(R,R) epoxide of trans-stilbene''
|
[[File:trans-stilbeneepoxideRRVCD.svg|150px]]
|{{DOI|10042/25997}}
|- align="center"
| ''(S,S) epoxide of β-methyl styrene''
|
[[File:methylstyreneepoxideSSVCD.svg|150px]]
|{{DOI|10042/25998}}
|- align="center"
| ''(R) epoxide of styrene''
|
[[File:styreneepoxideRVCD.svg|150px]]
|{{DOI|10042/26000}}
|- align="center"
| ''(S) epoxide of styrene''
|
[[File:styreneepoxideSVCD.svg|150px]]
|{{DOI|10042/25996}}
|- align="center"
| ''(1R,2S) epoxide of 1,2-dihydronaphthalene''
|
[[File:naphtepoxideRSVCD.svg|150px]]
|{{DOI|10042/25999}}
|}

The (R) and (S) epoxides of styrene can be seen to have a degree of symmetry about the centre axis. Particularly,
in the VCD spectrum for the (R) epoxide the peak at ~700 is positive, whilst that at ~1500 is negative, whereas
this is reversed for the (S) epoxide. With additional time, I would have searched for literature VCD spectra to compare.

====Using the (calculated) properties of transition state for the reaction====

'''Transition states for Shi epoxidation of trans-β-methyl styrene'''

{| class="wikitable"
|-
! Free energy G (Hartrees): R,R series !! Free energy G (Hartrees): S,S series !! Difference in energy (R,R)-(S,S) in Hartrees !! in kJ/mol !! K !! Enantiomeric excess
|-
| -1343.022970 || -1343.017942 || -0.005028 || -13.201015006 || 4.85x10^-3 || 99.0%
|-
| -1343.019233 || -1343.015603 || -0.003630 || -9.530565726 || 0.0213 || 95.8%
|-
| -1343.029272 || -1343.023766 || -0.005506 || -14.4560041 || 2.92x10^-3 || 99.4%
|-
| -1343.032443 || -1343.024742 || -0.007701 || -20.21897704 || 2.86x10^-4 || 99.9%
|}

On first inspection, without any further analysis, it appears that the R,R series of transition states for the Shi epoxidation of trans-β-methyl styrene are of lower energy than the S,S series of transition states. This suggests that the (R,R) epoxide of trans-β-methyl styrene would be preferentially formed over the (S,S) epoxide, which fits with both literature results<ref>Z-X. Wang, L. Shu, M. Frohn, Y. Tu, Y. Shi, Organic Syntheses, 2003, 80, 9</ref> and what I observed whilst in the wet lab 1S.

Steps I took to calculate enantiomeric excess:
* I found the difference in energy - dG - between each (R,R) and (S,S) transition state.
* I then converted the energy values from Hartrees (as is provided in the output files) into kJ/mol.
* Using dG=-RTlnK, and rearranging to give K=exp(-dG/RT) allows values of K to be found for each transition state (with R=8.314J/molK, and T=298K). K can be viewed as a ratio between the two possible products.
* I put K = 1-X/X, rearranged to X=1/1+K, where X is the mole fraction of 1 of the isomers. The enantiomeric excess is the fraction of 1 isomer - the fraction of the 2nd isomer.

The literature enantiomeric excess for Shi epoxidation of trans-β-methyl styrene is 91-92%. Although the calculated values for the enantiomeric excess of the transition states are higher than this, when combined it is brought down to 94%, closer to literature.
<ref>Z-X. Wang, L. Shu, M. Frohn, Y. Tu, Y. Shi, Organic Syntheses, 2003, '''80''', 9</ref>

'''Transition states for Jacobsen epoxidation of trans-β-methyl styrene'''

{| class="wikitable"
|-
! Free energy G (Hartrees): R,R series !! Free energy G (Hartrees): S,S series !! Difference in energy (R,R)-(S,S) in Hartrees !! in kJ/mol !! K !! Enantiomeric excess
|-
| -3383.253816 || -3383.262481 || 0.008665 || 22.7499592|| 1.03x10^-4 || 99.97%(!)
|-
| -3383.254344 || -3383.257847 || 0.003503 || 9.1971272 || 0.0244 || 95.2%
|}

Again, by first inspection, this time it is the S,S series of transition states that are of lower energy, suggesting that the (S,S) epoxide would be formed preferentially. I again calculated the enantiomeric excess for the transition states.

So, for a trans alkene, Shi epoxidation supposedly leads to the (R,R) epoxide and Jacobsen epoxidation leads to the (S,S) epoxide. How about for a cis alkene?

'''Transition states for Shi epoxidation of 1,2-dihydronaphthalene'''

{| class="wikitable"
|-
! Free energy G: R,S series !! Free energy G: S,R series !! Difference in energy (R,S)-(S,R)
|-
| -1381.120782 || -1381.131343 || 0.010561
|-
| -1381.125886 || -1381.116109 || -0.009777
|-
| -1381.134059 || -1381.126059 || -0.008
|-
| -1381.126722 || -1381.136239 || 0.009517
|}

Here, there is no immediately clear way to determine which of the series is of lower energy. I would expect it to be the (R,S) series, but the pair with the largest energy difference is that with the (S,R) transition state lower in energy.

'''Transition states for Jacobsen epoxidation of cis-β-methyl styrene'''

{| class="wikitable"
|-
! Free energy G: R,S series !! Free energy G: S,R series !! Difference in energy (R,S)-(S,R)
|-
| -3383.251060 || -3383.259559 || 0.008499
|-
| -3383.250270 || -3383.253442 || 0.003172
|}

This time it is clear that the (S,R) series of transition states is more stable than the (R,S) series.

====Investigating the non-covalent interactions in the active-site of the reaction transition state====

I chose one of the included transition states and subjected it to a NCI analysis. The transition state used is the second in the (R,R) series for the Shi epoxidation of trans-β-methyl styrene (chosen more or less randomly.) The result is pictured here, with the Shi catalyst to the left of the image and the alkene to the right.

[[Image:transitionstate2SPannotated.jpg|500px|centre|frame|NCI model of the second transition state of the Shi epoxidation of trans-β-methyl styrene in (R,R) series]]

Just by looking at the image, it is clear that there are very few repulsive interactions, and an extended degree of attractive interactions. The bond forming between the two molecules can be seen. It is believable that the pictured transition state is indeed particularly low in energy and would lead to the (R,R) product preferentially over the (S,S) product.

[[Image:Friday2.jpg|200px|centre|frame|NCI model of the second transition state of the Shi epoxidation of trans-β-methyl styrene in (S,S) series]]

This is the corresponding (S,S) transition state to that above. Although there is still a very large degree of attractive
interactions, there is slightly more repulsive interactions; definitely more of the slightly repulsive regions (yellow)
have a greater amount of strongly repulsive character (red) than before, raising the energy of this transition state above
that of the other. However, of the entire series, these are two of the transition states which are most similar in energy, hence may not have been the best pair to analyse(!). It would seem that it is the relative energies of the other transition states in the same series that may have more of an effect leading to the preferential production of one isomer over the other.

====Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state====

I used the same transition state as for the NCI analysis, and subjected it to a QTAIM analysis. The model shows BCPs - Bond topological Critical Points - as the yellow spheres between two nuclei. Those BCPs associated with a solid white line indicate the presence of a bond, whereas those with a dashed line demonstrate a weaker, non-covalent interaction. A molecule of trans-β-methyl styrene is in the bottom right corner of the frame, with the Shi catalyst above it. The weak, non-covalent interactions are those between the two molecules in this transition state, whilst the covalent interactions are those known to be in the molecules (and are hence less interesting.)

[[File:QTAIM.jpg|200px|centre|frame|QTAIM analysis of the second transition state of the Shi epoxidation of trans-β-methyl styrene in (R,R) series]]

I have labelled a few BCPs which are particularly interesting:
*1. This weak, non-covalent BCP has a more pronounced curve than any other.
*2. This BCP demonstrates that the BCP can be positioned much closer to one atom than the other.
*3. This non-covalent BCP is, at first glance, the one forming between the two furthest away atoms, both within the catalyst itself.
*4,5,6 Alongside 3, these BCPs are between atoms that one might not necessarily expect to interact due to their distance and geometry.

====Suggesting new candidates for investigations====

I carried out a search on Reaxys for epoxides with optical rotary power greater than 500 or less than -500. This returned
a surprisingly large number of results. One such epoxide is pictured below is called trans-1-(p-Chlorphenyl)-2-phenylethenoxid.
It has an optical rotary power of 780 deg. <ref>P. M. Dansette, H. Ziffer, D. M. Jerina, Tetrahedron, 1976, '''32''', 2071-2074</ref>
Its corresponding alkene is also pictured below, and is called 1-(4-chlorophenyl)-2-phenyl-ethylene. It at least produces one search result on Sigma Aldrich which is more than the other alkenes I tried(!).

[[Image:Epoxide-alkene.jpg|500px|centre|thumb|Found epoxide and alkene]]

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T16:19:42Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

In this mini project, four aromatic molecules will be explored: benzene, boratabenzene, pyridinium and borazine.

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

NBO analysis can also be carried out:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds as calculated. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been drawn and included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding) from the above diagram. Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

Boratabenzene is a molecule of benzene with one of the carbon atoms exchanged for a boron atom. The molecule carries a negative charge.

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. This is slightly longer than in benzene, suggesting slightly weaker bonds. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °, portraying the distortion in the ring, unlike benzene which has a regular configuration of all 120 ° angles.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

Pyridinium is a benzene molecule with one of the carbon atoms exchanged for a nitrogen. The molecule carries a positive charge.

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). This is slightly shorter than in benzene, suggesting that the bonds have been made stronger upon addition of the more electronegative atom. Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °, similar to boratabenzene.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

The ring of borazine is made up of alternating boron and nitrogen atoms.

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å (a literature value is 1.44 Å<ref>P. B. Saxena, ''Chemistry of Interhalogen Compounds''. Discovery, Delhi, 2007, pp. 75</ref>). There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|thumb|800px|Diagram portraying charge positions]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para- to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho- and para- positions to the boron. This leaves the meta- position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta- positions to the nitrogen has more negative charge than the para- position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para- position, but none with the positive charge on the meta- positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules (collected in the table above). This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative charge on boratabenzene or on the positively charged pyridinium, the lone pair of the nitrogen. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

This mini-project has allowed exploration of the topic of aromaticity through carrying out calculations on four different aromatic molecules. The calculations as run all successfully found optimised minimums for the molecules, using the same, relatively simple, basis set each time (6-31G(d,p). This was appropriate for these molecules, each of which contains only 2nd row elements. However, it is not the case that further, more complex calculations could have given better results (this can be seen in the calculated bond lengths, each of which is close (or equal) to literature, but there is room for improvement).

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T16:14:19Z

Sjp211: /* MINI PROJECT - AROMATICITY */

Rep:Mod:XYZ12394

2013-11-22T16:08:19Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

In this mini project, four aromatic molecules will be explored: benzene, boratabenzene, pyridinium and borazine.

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

NBO analysis can also be carried out:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds as calculated. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been drawn and included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding) from the above diagram. Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

Boratabenzene is a molecule of benzene with one of the carbon atoms exchanged for a boron atom. The molecule carries a negative charge.

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °, unlike benzene which has a regular configuration of all 120 ° angles.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

Pyridinium is a benzene molecule with one of the carbon atoms exchanged for a nitrogen. The molecule carries a positive charge.

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °, similar to boratabenzene.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

The ring of borazine is made up of alternating boron and nitrogen atoms.

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å (a literature value is 1.44 Å<ref>P. B. Saxena, ''Chemistry of Interhalogen Compounds''. Discovery, Delhi, 2007, pp. 75</ref>). There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|thumb|800px|Diagram portraying charge positions]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para- to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho- and para- positions to the boron. This leaves the meta- position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta- positions to the nitrogen has more negative charge than the para- position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para- position, but none with the positive charge on the meta- positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules (collected in the table above). This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative charge on boratabenzene or on the positively charged pyridinium, the lone pair of the nitrogen. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:59:43Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

In this mini project, four aromatic molecules will be explored: benzene, boratabenzene, pyridinium and borazine.

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å (a literature value is 1.44 Å<ref>P. B. Saxena, ''Chemistry of Interhalogen Compounds''. Discovery, Delhi, 2007, pp. 75</ref>). There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|thumb|800px|Diagram portraying charge positions]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules (collected in the table above). This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative charge on boratabenzene or on the positively charged pyridinium, the lone pair of the nitrogen. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:56:01Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å (a literature value is 1.44 Å<ref>P. B. Saxena, ''Chemistry of Interhalogen Compounds''. Discovery, Delhi, 2007, pp. 75</ref>). There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|thumb|800px|Diagram portraying charge positions]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules (collected in the table above). This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative charge on boratabenzene or on the positively charged pyridinium, the lone pair of the nitrogen. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:51:48Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å (a literature value is 1.44 Å<ref>P. B. Saxena, ''Chemistry of Interhalogen Compounds''. Discovery, Delhi, 2007, pp. 75</ref>). There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|thumb|800px|Diagram portraying charge positions]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:47:27Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å (a literature value is 1.44 Å<ref>P. B. Saxena, ''Chemistry of Interhalogen Compounds''. Discovery, Delhi, 2007, pp. 75</ref>). There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:42:03Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|MO diagram for benzene]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:39:59Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic. Although the energy difference between the molecules is fairly small when using A.U., it is to be remembered that in more conventional units - kJ/mol - the differences would be large.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:35:24Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å (a fit with literature<ref>P. M. Dewick, ''Essential of Organic Chemistry'', Wiley, Chichester, 2006, pp. 44</ref>) and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks<ref>J. C. Kotz, P. M. Treichel, J. R. Townsend, ''Chemistry and Chemical Reactivity'', Thomson Higher Education, Belmont, 7th edn., 2009, pp. 432</ref>) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-22T15:24:29Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom. This means that the pi type C=C bonds are not in fixed positions. In reality, each carbon-carbon bond is somewhat in between that of a single and double bond. The pi type carbon bonds explored in the file from the calculation have an occupancy significantly below 1, as these bonds are instead spread over all six carbon atoms.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-21T19:56:43Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, ''Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters'', World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, ''Chemistry of P-Block Elements'', Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-21T19:55:33Z

Sjp211:

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å. This fits with literature (quoting a bond length of 1.191 Å). <ref>C-Y. Ng, Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters, World Scientific, Singapore, 1991, pp. 29</ref>

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å<ref>K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913</ref> (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å (compared to a literature value of 1.89 Å)<ref>M. Satake, S. A. Iqbal, Chemistry of P-Block Elements, Discovery Publishing House, India, 1995, pp. 38</ref> and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å (compared to literature of 1.03 Å<ref>M. Elanany, P. Selvam, A. Endou, M. Kubo, A. Miyamoto, Studies in Surface Science and Catalysis, 2004, '''154''', 1763-1768</ref>) and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

==References==
<references />

Rep:Mod:XYZ12394

2013-11-21T19:23:05Z

Sjp211:

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 8 - 2e' || 0.17929
|-
| 7 - 2e' || 0.17929
|-
| 6 - 3a1' || 0.16839
|-
| 5 - <pre>A2''</pre>|| -0.06605
|-
| 4 - 1e' || -0.35079
|-
| 3 - 1e' || -0.35079
|-
| 2 - 2a1' || -0.51254
|-
| 1 - 1a1' (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T19:15:50Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

{| class="wikitable"
|-
! Molecular orbital !! Energy (A.U.)
|-
| 7 || 0.17929
|-
| 6 || 0.17929
|-
| 5 || 0.16839
|-
| 4 || -0.06605
|-
| 3 || -0.35079
|-
| 2 || -0.51254
|-
| 1 (core) || -6.77140
|}

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T19:08:07Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Image of the vibration !! Description of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] || All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] || Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] || All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] || 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] || 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T19:04:16Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the opposite direction concertedly - this is referred to as out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - referred to as in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - this stretching mode is referred to as breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa; this is a stretching mode || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - this is referred to as asymmetrical stretching|| 2716 || 126 || E'
|}

It should be noted that the bending vibrational are all of lower energy than the stretching vibrational modes (less energy is needed to bend a bond than to stretch it.)

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The value of the frequencies are very different for BH3 compared to GaBr3. The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 (and hence less energy is required to stretch or bend the bonds) and the much larger reduced mass of that molecule.
There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity.

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T18:55:56Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T18:53:40Z

Sjp211:

INORGANIC COMPUTATIONAL MODULE: SAMUEL PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T18:53:17Z

Sjp211:

INORGANIC COMPUTATIONAL MODULE: SAM PAGE (CID: 00687062)

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T18:52:33Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. The signs of a converged job are small values and a column full of 'YES' under 'Converged?'. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}.

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-21T18:50:01Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]].

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}.

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

The population analysis file is linked to here: {{DOI|10042/26095}}.

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-19T19:26:35Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624 A.U.''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393 A.U.''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992 A.U.''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913 A.U.''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992 A.U.''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063 A.U.''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934 A.U.''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193 A.U.''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549 A.U.''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040 A.U.''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157 A.U.''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040 A.U.''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-19T19:25:17Z

Sjp211: /* COMPULSORY SECTION */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

The population analysis file is linked to here: {{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

The population analysis file is linked to here: {{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-19T19:24:07Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
The population analysis file is linked to here: {{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-19T19:22:33Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene. (This is mainly true for the entire set of molecular orbitals, with some variation; for example, the LUMO of benzene is more stable than that of borazine). This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-19T19:18:22Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). These are MOs 7,8 and 9. These were chosen for their simplicity, allowing general ideas to be explored more clearly.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon. One interesting feature present in each of the MO 7s is the slight indentation in the MO, demonstrating that electron density is being preferentially pulled towards the plane of the ring.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

It has been seen that for the MOs chosen above, the energy ordering each time had pyridinium lowest, then borazine, benzene and boratabenzene, This is reflected in the overall energies of the molecules, found early on after optimisation of the molecules. This showed that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene. In other words, pyridinium is the most aromatic of all the molecules. There are several definitions of aromaticity; Huckel's rule states that there must be 4n + 2 delocalised electrons; 6 for benzene, and indeed each of the molecules thanks to the presence of the negative or positive charge. This means that each of these molecules is isoelectronic.

Rep:Mod:XYZ12394

2013-11-19T19:05:59Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene. The meta positions to the nitrogen has more negative charge than the para position; again, this can be rationalised by drawing resonance forms, which feature a form with the positive charge on the para position, but none with the positive charge on the meta positions. Because pyridinium has a positive charge, of course this means that there is less negative charge in the ring itself than in benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The theory behind molecular orbitals 8 and 9 is similar to that of 7, however an additional interest is the degeneracy of these MOs in benzene. These MOs are still strongly bonding (although of not insignificantly higher energy than MO 7) and this time feature a node halfway between a set of either 3 or 4 sets of carbon and hydrogen bonding interactions. For benzene, it can be seen that these MOs are exactly symmetric. In boratabenzene, however, there is a loss of degeneracy with MOs 8 and 9, with an energy difference of 0.0585 A.U. This loss of degeneracy can clearly be seen in the lack of symmetry in the two MOs. Unsurprisingly, it is the MO which includes a contribution from the B atom which is of higher energy; the other contains only carbon (and hydrogen) orbitals, lacking the more electropositive B atom. In pyridinium, too, there is loss of degeneracy between MOs 8 and 9. Their energy difference this time is only 0.03392 A.U. Using the same reasoning, it is the MO that has more contribution from the N atom that is lower in energy, due to the stabilising effect of the more electronegative N atom. In borazine, the degeneracy with MOs 8 and 9 is restored, as might be expected. Although the forms of the MOs look slightly more unusual, each features the same contribution from the B and N atoms, and is hence of equal energy. The ordering of MOs between molecules is as for MO 7 (pyridinium lowest, then borazine, benzene and boratabenzene) which is not surprising.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T18:40:51Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs 17, 20 and 21 (bonding) and 22, 23 and 27 (anti-bonding). Aromatic systems are those which have a ring system of unexpectedly high stability, due to the delocalisation of electrons throughout the ring; for benzene, each carbon atom has an unpaired electron in its pz orbital and these electrons are said to be delocalised, or spread around the ring, not attached to any particular carbon atom.

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself (in the pi cloud) and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. This can be rationalised by considering the possible resonance forms for the anion, drawn below. There are canonical forms in which the negative charge is on the B atom, and also on the carbons at ortho and para positions to the boron. This leaves the meta position with the lowest negative charge of all carbons. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T18:32:44Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

The standard MO diagram for benzene (that found in most textbooks) includes only the 6 pz orbitals on the carbon atoms, ignoring the sigma orbitals. In effect, this is limiting the above MO diagram to just MOs

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T18:30:50Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|centre|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T18:30:16Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

[[Image:Resonance forms.png|centre|thumb|700px|Diagram showing resonance forms of boratabenzene and pyridinium]]

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon.

[[Image:aromaticity mos.png|centre|thumb|700px|Cartoon comparing molecular orbital 7]]

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

File:Resonance forms.png

2013-11-19T18:24:08Z

Sjp211:

File:Aromaticity mos.png

2013-11-19T18:23:16Z

Sjp211:

File:Aromaticity mos.cdx

2013-11-19T18:21:17Z

Sjp211:

Rep:Mod:XYZ12394

2013-11-19T07:48:12Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then borazine, benzene, boratabenzene. The electronegativity of N in pyridinium stabilises the orbitals of N, and hence of the MO itself. Boron has the opposite effect in being more electropositive than carbon.

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T07:46:03Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is involved and in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution. This is all reflected in the images above: for benzene, the electron cloud is spread evenly over the ring; in boratabenzene there is a lack of electron density on the B; in pyridinium an increased electron density on the N; and in borazine, the MO is as in benzene, but with undulating electron density around the ring as each B and N is passed. Molecular orbital 7 is of lowest energy for pyridinium; then

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T07:41:34Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

Molecular orbital 7 is that in which each C and H s orbital is in phase and is therefore totally bonding. For benzene, there is equal contribution from each C 2s orbital; on the MO diagram, each orbital is depicted as having the same size. This would not be the case for boratabenzene; carbon is more electronegative than boron and hence its orbitals sit at lower energy, meaning that this bonding orbital would have more contribution from the C 2s orbitals than the B 2s orbitals; the B 2s orbital would be drawn smaller than those of C on an MO diagram. This would be opposite to pyridinium, where the more electronegative N would have more stable orbitals and hence a greater contribution to the MO. In borazine, each nitrogen would have the same, larger contribution compared to each boron which would have the same, smaller contribution.

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

Rep:Mod:XYZ12394

2013-11-19T07:20:29Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:benzene mo diagram.png|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.

File:Benzene mo diagram.png

2013-11-19T07:19:12Z

Sjp211:

File:Benzene mo diagram.cdx

2013-11-19T07:18:38Z

Sjp211:

Rep:Mod:XYZ12394

2013-11-18T21:31:22Z

Sjp211: /* MINI PROJECT - AROMATICITY */

INORGANIC LAB SAM PAGE

==COMPULSORY SECTION==

'''BH3 optimisation'''

The first stage was to create a molecule of BH3 in Gaussview, which I proceeded to optimise using a B3LYP method and a 3-21G basis set. The summary table is included here:

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
3-21G
|- align="center"
| '''Final energy (a.u.)'''
|
-26.46226429
|- align="center"
| '''Gradient (a.u.)'''
|
0.00008851
|- align="center"
| '''Dipole moment'''
|
0.003 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
34 secs
|}

The optimisation file is linked to [[media:SP3_BH3_OPT.LOG| here]].

To check that the optimisation job truly did converge, it is useful to check the Item table found in the output file. This is included here:

<pre>Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
-- Stationary point found.</pre>

'''BH3 optimisation: using a better basis set'''

Now, it possible to use the optimised geometry above to carry out a second optimisation with a higher level basis set, this time 6-31G(d,p).

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-26.61532360
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000707
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
32 secs
|}

The optimisation file is linked to [[media:SPBBS_BH3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised bond angle is found to be 120 ° and the optimised bond length is 1.19 Å.

It is possible to look at the energies obtained from each optimisation. For the 3-21G optimisation, the total energy is -26.46226429 A.U.; for the -26.61532360 A.U. This is a difference of 0.15305931 A.U., or 401.86kJ/mol. However, it is the case that one cannot compare the energies of structures which have been computed using different basis sets, as is the case here.

'''GaBr3 optimisation'''

This time a molecule of GaBr3 was created in Gaussview. An optimisation was calculated; the differences this time being that the symmetry was constrained to D3h, and a new basis set LanL2DZ was used. The calculation was submitted to the HPC service.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
LANL2DZ
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-41.70082783
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000011
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
D3H
|- align="center"
| '''Calculation time'''
|
8 secs
|}

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26071
{{DOI|10042/26071}}

<pre>Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-5.834383D-13
Optimization completed.
-- Stationary point found.</pre>

The optimised Ga-Br bond length is found to be 2.35 Å, and the optimised Br-Ga-Br bond angle 120 °.

As a check, a reference Ga-Br bond length is 2.353 Å (compared to 2.35018 Å calculated). There is no meaningful difference between the two lengths, so this literature value definitely suggests that the calculated length is reasonable. The reference is: K. Balasubramanian, J. X. Tao, D. W. Liao, J. Chem. Phys., 1991, 95, 4905-4913.

'''BBr3 optimisation'''

Starting from the optimised file for BH3, a molecule of BBr3 was created and optimised (again using the HPC service). This time the basis set GEN was used, allowing the B atoms (light) and the Br atoms (heavy) to be treated separately, with pseudo-potentials used for the Br atoms.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
Gen
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-64.43644651
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000941
|- align="center"
| '''Dipole moment'''
|
0.0002 D
|- align="center"
| '''Point group'''
|
CS
|- align="center"
| '''Calculation time'''
|
35 secs
|}

The optimisation file is linked to [[media:SP3_BBR3_OPT.LOG| here]].

<pre>Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-2.424079D-09
Optimization completed.
-- Stationary point found.</pre>

The optimised B-Br bond length is 1.93 Å and the optimised Br-B-Br bond angle is 120 °.

'''Comparisons'''

{| class="wikitable"
|-
! BH3 bond length (Å)!! BBr3 bond length (Å)!! GaBr3 bond length (Å)
|-
| 1.19 || 1.93 || 2.35
|}

For the same centre (BH3 and BBr3), changing the ligand from H to Br increases the bond length significantly. At first glance, this seems sensible; Br is after all a much larger atom than H, and for steric reasons one would expect the Br atoms to be further away from the B atom, which is itself relatively very small. The bond angles for each molecule are 120 ° (the arrangement whereby the ligands are as far away as possible), so to maintain this, the Br atoms are forced further away than the corresponding H atoms. B and H have radii much closer in size than B and Br, hence there is better orbital overlap, leading to stronger bonds.

Another consideration is the electronegativity of H and Br. Br is more electronegative than H; whilst the electronegativities of B and H are very similar, Br is considerably more electronegative than B. Hence, B and H will be happy to share electrons and form a strong covalent bond, whilst the B-Br bond will have some more ionic character and have a higher bond polarity. H has just the one electron, and hence acts as a one electron donor. Br- behaves similarly due to its single negative charge.

For the same ligand (BBr3 and GaBr3), changing the centre from B to Ga increases the bond length significantly. Whilst B and Ga are both Group 13 elements, and hence have three valence electrons each, Ga is two periods below B and therefore much larger. In fact, Ga and Br are both in the same period and hence their radii are much more similar than for B and Br. Despite this, Ga and Br have very large orbitals and hence there is poor orbital overlap. In this case, changing the centre has less of an effect on the bond length than changing the ligand. However, the electronegativity difference between Ga and Br is very large, and hence the Ga-Br bond has a large ionic component i.e. the bond is polar.

*In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
*What is a bond?

On Gaussview, a bond is only displayed as a line between two atoms when two atoms have a separation within a certain distance (pre-defined by the program)- if any two atoms are placed further away than this set distance, no bond is shown; two atoms closer together than this set distance are joined by a bond. Clearly, this is a huge approximation; it is true that if two atoms are very far apart then they will interact more weakly than if they are very close together, but it is not realistic for this behaviour to be defined as switching on/off at a defined point; it is a simplification. The display of a bond or not in Gaussview has no effect on the way it treats the molecule: it is more of a display 'quirk'.

A chemical bond is something open to interpretation: in its most basic form, an attractive interaction between two atoms, or some sort of force holding two atoms together. This electrostatic force does indeed have a distance dependence. However, there are a vast array of different bonding types: covalent, ionic, van der Waals, Hydrogen... These will all have different strengths and thus different contributions to the stability of a molecule.

'''Frequency analysis for BH3'''

Using the optimisation file (6-31G(d,p) basis set) as completed before for BH3, it is possible to continue further and carry out a frequency analysis.

The low frequencies labelled in the output file (included here) are important. The 6 frequencies in the first line are those of the 3N-6 vibrational frequencies of each molecule. It is required for these to be low, especially in comparison to the first vibration listed in the second line.

<pre>Low frequencies --- -3.6020 -1.1356 -0.0054 1.3734 9.7035 9.7697
Low frequencies --- 1162.9825 1213.1733 1213.1760</pre>

The optimisation file is linked to [[media:SP_BH3_FREQ2.LOG| here]]

'''Animating the vibrations'''

From the frequency analysis, it was possible to animate the vibrations, which are summarised in the table here.

{| class="wikitable"
|-
! No. !! Form of the vibration !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || [[Image:BH3 vib 1 sp2.png|150px]] All H atoms move up and down together in a concerted motion, with the B atom moving in the oppositedirection concertedly - out-of-plane bending || 1163 || 93 || <pre>A2''</pre>
|-
| 2 || [[Image:BH3 vib 2 sp.png|150px]] 2 H atoms move in and out together in a concerted motion, with the other B and H atoms moving together up and down - in-plane bending || 1213 || 14 || E'
|-
| 3 || [[Image:BH3 vib 3 sp.png|150px]] Each H atom bends independently || 1214 || 14 || E'
|-
| 4 || [[Image:BH3 vib 4 sp.png|150px]] All H atoms move in and out together in a concerted motion; the B atom is stationery - breathing || 2582 || 0 || A1'
|-
| 5 || [[Image:BH3 vib 5 sp.png|150px]] 2 H atoms move in and out; as one moves in, the other moves out and vice versa || 2716 || 126 || E'
|-
| 6 || [[Image:BH3 vib 6 sp.png|150px]] 2 H atoms move in and out together in a concerted motion; the other H moves up as the others move out, and vice versa - asymmetrical stretching|| 2716 || 126 || E'
|}

The computed IR spectrum is here:

[[Image:BH3 IR.jpg|500px|left|frame|IR spectrum for BH3]]

Although there are six listed frequencies, the two sets of E' frequencies occur at very almost or exactly the same frequency value and are hence seen as just one peak. In addition, the A1' frequency has zero intensity. This is because this vibration is IR inactive, as there is no change of dipole moment. This leaves just 3 peaks visible.

'''Frequency analysis for GaBr3'''

A similar frequency analysis can be carried out for GaBr3.

<pre> Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982</pre>

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26086
{{DOI|10042/26086}}

{| class="wikitable"
|-
! No. !! Frequency (cm-1) !! Intensity !! Symmetry D3h point group
|-
| 1 || 76 || 3 || E'
|-
| 2 || 76 || 3 || E'
|-
| 3 || 100 || 9 || <pre>A2''</pre>
|-
| 4 || 197 || 0 || A1'
|-
| 5 || 316 || 57 || E'
|-
| 6 || 316 || 57 || E'
|}

[[Image:GaBr3 IR.png|100px|left|frame|IR spectrum for GaBr3]]

'''Comparing the vibrational frequencies of BH3 and GaBr3'''

{| class="wikitable"
|-
! BH3: Frequency (cm-1) !! Intensity !! Symmetry !! GaBr3: Frequency (cm-1) !! Intensity !! Symmetry
|-
| 1163 || 93 || <pre>A2''</pre> || 76 || 3 || E'
|-
| 1213 || 14 || E' || 76 ||3 || E'
|-
| 1213 || 14 || E' || 100 || 9 || <pre>A2''</pre>
|-
| 2582 || 0 || A1' || 197 || 0 || A1'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|-
| 2716 || 126 || E' || 316 || 57 || E'
|}

The frequencies for GaBr3 are much lower than those of BH3. This can be attributed to the weaker bonds present in GaBr3 and the much larger reduced mass of that molecule.
The value of the frequencies are very different for BH3 compared to GaBr3... There has been a slight reordering of modes; although the A2 and E' modes have a set of similar frequencies with the A1' and E' modes having another set of similar frequencies but at higher energy, for BH3, the A2 frequency is of lower energy than its E' brothers, for GaBr3 this order has been reversed.
The spectra are similar in that each has 3 peaks. 2 of these appear close together at lower frequency and are of lesser intensity. The 1 remaining peak appears at much higher frequency and is of much higher intensity. BONDING/ANTIBONDING ORBITALS

*Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
This allows direct comparison between the results from the calculations.
*What is the purpose of carrying out a frequency analysis?
Frequency analysis allows us to confirm that we truly have our optimised our structure as a minimum. The diagnostic information givn is that the frequencies should all be positive for a minimum; if any are positive, this suggests transition state or a failed optimisation. The low frequencies should be low. Frequency analysis allows production of an IR spectrum, and for the vibrations of the molecule to be explored.
*What do the "Low frequencies" represent?
Each molecule (that is not linear) has 3N-6 degrees of vibrational modes; the low frequencies are those 6 and are the motions of the centre of mass of the molecule. These should be as small as possible, and are minimised with increasingly good optimisation.

'''Molecular orbitals of BH3'''

https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26095
{{DOI|10042/26095}}

There are no significant differences between the real and LCAO orbitals, suggesting that qualitative MO analysis is both very accurate and useful.

[[Image:BH3 MO DIAGRAM 2.png|600px]]

'''NBO analysis'''

NH3

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.634443D-09
Optimization completed.
-- Stationary point found.</pre>

The optimisation file is linked to [[media:WED NH3 OPT.LOG| here]].
The frequency analysis file is linked to [[media:WED NH3 FREQ.LOG| here]].
https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26112
{{DOI|10042/26112}}

The optimised bond length is 1.02 Å and the optimised bond angle is 106 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-56.55776872
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00000878
|- align="center"
| '''Dipole moment'''
|
1.8464 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
36 secs
|}

<pre>Low frequencies --- -6.8215 0.0013 0.0015 0.0018 11.3351 16.1518
Low frequencies --- 1089.3553 1693.9211 1693.9586</pre>

[[Image:NH3 charge dist.png|300px]]

Colour range: -1.132 to +1.132.

Specific NBO charges: N: -1.132, H: +0.377

'''NH3BH3'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-83.22468889
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00005803
|- align="center"
| '''Dipole moment'''
|
5.5626 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
50 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001017 0.001800 YES
RMS Displacement 0.000224 0.001200 YES
Predicted change in Energy=-1.130217D-07
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -12.0985 -0.0014 -0.0009 -0.0006 9.2098 10.2976
Low frequencies --- 262.8357 631.2185 638.0529</pre>

The optimisation file is linked to [[media:WED_NH3BH3_OPT HIGH.LOG| here]].
The frequency analysis file is linked to [[media:WED_NH3BH3_FREQ.LOG| here]].

*E(NH3)= -56.55776856 A.U.
*E(BH3)= -26.61532360 A.U.
*E(NH3BH3)= -83.22468889 A.U.

*ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22468889)-((-56.55776872)+(-26.6152360))= -0.05168417 A.U.
*To convert from A.U. to kJ/mol, it is necessary to multiply the calculated figure by 2625.5, giving ΔE = -135.7 kJ/mol. This is in the same 'ballpark' as typical bond energy values. This energy value is only as a result of the enthalpy change (for these calculations, entropy is ignored). Hence, NH3BH3 is energetically more stable than the reactants. This analysis suggests that the B-N bond that has been formed adds stability; B-N is a strong bond.

==MINI PROJECT - AROMATICITY==

'''Benzene'''

As a starting point, a benzene molecule was created and optimised.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-232.25820396
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003423
|- align="center"
| '''Dipole moment'''
|
0 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
55 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000111 0.001800 YES
RMS Displacement 0.000051 0.001200 YES
Predicted change in Energy=-2.326716D-08
Optimization completed.
-- Stationary point found.</pre>

<pre> Low frequencies --- -5.4822 -2.4429 -0.0006 0.0008 0.0009 5.2613
Low frequencies --- 414.4720 414.5447 621.1074</pre>

The optimisation file is linked to [[media:SP_BENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BENZENE_FREQ.LOG| here]].
{{DOI|10042/26118}}

As before, some simple information can quickly be found. Each C-C bond length is 1.40 Å and each C-H bond 1.09 Å. The C-C-C bond angle is 120 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:benzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:benzene_nbo_numbers.png|300px]]
|}

The charge range is from -0.238 to +0.238.

Further analysis of the log file from this calculation more or less confirms what is known about benzene already. There are two types of C-C bonds. One has equal contribution from each C (50% each) and the orbitals involved are 35%s and 65%p, clearly suggesting sp2 hybrid orbitals. The other C-C bond again has equal contribution from each carbon, this time with p orbitals. This represents the delocalisation of the pi electrons. The C-H bonds are 1.98 Å, this time with 62% contribution from C (38% from H), formed by the overlap of a C sp2 orbital and a H s orbital.

The first C-C bond has an occupancy of 2 electrons, as expected; however the pi type bond has an occupancy of 1.66, significantly below 2. This reinforces the idea of delocalisation.
Under the section 'Second Order Perturbation Theory Analysis of Fock Matrix in NBO basis' which describes MO mixing, there are six E(2) energies greater than 20 kcal/mol. Each of the bonding orbitals C1-C6, C2-C3 and C4-C5 mixes with the two other anti-bonding orbitals (i.e. for C1-C6 bonding orbital, there is mixing with C2-C3 and C4-C5 anti-bonding orbitals). These all have E(2) energies of 20.38/20/39 kcal/mol, which adds a great deal of stability to the molecule. From the summary section, it is shown that the sp2 C-C bonds are of lowest energy (~-0.681), followed by C-H bonds (~-0.51) then pi C-C bonds (~-0.24).

The MO diagram for benzene including both sigma and pi orbitals has been included below.

[[Image:mo diagram benzene.png|thumb|700px|mo]]

'''Boratabenzene'''

[[Image:boratabenzene_img.png|frame|150px|Boratabenzene]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
-1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-219.02052295
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00003609
|- align="center"
| '''Dipole moment'''
|
2.8457 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 7 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000061 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000277 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.727712D-08
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -7.0096 -0.0005 0.0007 0.0010 1.2981 6.0551
Low frequencies --- 371.2955 404.4402 565.1118</pre>

The optimisation file is linked to [[media:SP_BORATABENZENE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORATABENZENE_FREQ.LOG| here]].
{{DOI|10042/26133}}

For boratabenzene, the C-C bond lengths are 1.41 Å or 1.40 Å when one of the carbons is attached to attached to the B. The C-H bonds are all 1.09 or 1.10 Å. The C-B bond is 1.51 Å and the B-H bond is 1.22 Å. The bond angles range from 116 - 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:boratabenzene_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:boratabenzene_nbo_numbers.png|300px]]
|}

The charge range is -0.588 to +0.588.

Looking again at the NBO log file, the two C-C bonds and the C-H bonds are as before. For the two C-B bonds, the C contribution is 67% and B contribution 33%, each formed by sp2 orbitals from each atom. The B-H bond has 55% H contribution (s) and 45% B contribution (sp2.

In addition, there is a lone pair labelled as being in a p orbital on a C atom, with an occupancy of a little over 1; also, there is an anti-bonding lone pair in a p orbital on the B atom with an occupancy of under 1. This is trying to accommodate for the negative charge of the boratabenzene anion.

Some of the E(2) energies in boratabenzene are extremely high. Both the C2-C3 and C4-C5 bonds mix with the two lone pairs to give E(2) = ~24 (LP* B) and E(2) = ~37 (LP C). Each lone pair mixes with anti-bonding C4-C5 and C2-C3 orbitals to give E(2) = ~71 (LP C) and E(2) = ~180(!) (LP* B).

The energy ordering of the bonds has been altered too. The sp2 C-C bond is still most stable (-0.47), followed by C-B (-0.32), C-H (-0.31), B-H (-0.18) and pi C-C (-0.02). The lone pairs are at 0.1 and 0.22 for LP C and LP* B respectively.

'''Pyridinium'''

[[Image:pyridinium_img.png|frame|150px|Pyridinium]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
1
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-248.66806081
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00004820
|- align="center"
| '''Dipole moment'''
|
1.8720 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1 m 31 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000086 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000682 0.001800 YES
RMS Displacement 0.000208 0.001200 YES
Predicted change in Energy=-1.056565D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -9.5599 -5.3753 -0.0011 0.0003 0.0012 3.8264
Low frequencies --- 391.9440 404.3126 620.2380</pre>

The optimisation file is linked to [[media:SP_PYRIDINIUM_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_PYRIDINIUM_FREQ.LOG| here]].
{{DOI|10042/26134}}

For pyridinium, there are two C-C bond lengths: 1.40 and 1.38 Å (when one of the carbons is attached to the N). Each C-H bond length is 1.08 Å, each C-N bond is 1.35 Å and the N-H bond is 1.02 Å. The bond angles range from 117 to 124 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:pyridinium_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:pyridinium_nbo_numbers.png|300px]]
|}

The charge range is -0.486 to +0.486.

From the NBO analysis, it is found that the C-N bond has 37% from the C and 63% from the N. The orbital contributions suggest a sp3 C orbital(!) and a N sp2 orbital. The pi type bond between C and N is only 28% C and 72% N. The H-N bond is 25% H (s) and 75% N (sp3(!)).

This time, there are two sets of orbital mixes with E(2)>20. Bonding C1-C2 and anti-bonding C4-C5 has E(2)=20.68; bonding C3-N12 and anti-bonding C1-C2 has E(2)=20.25; bonding C4-C5 and anti-bonding C3-N12 has E(2)=47.85; anti-bonding C3-N12 and anti-bonding C4-C5 has E(2)=49.28.

The most stable bonds are the C-N bonds (non-pi) (-1.06), followed by C-C (-0.93), C-N (pi) (-0.57), C-C (pi) (-0.47), N-H (-0.89) and C-H (-0.75).

'''Borazine'''

[[Image:borazine_img2.png|thumb|500px|Borazine]]

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Name'''
| width="150" | '''Structure'''

|- align="center"
| '''File type'''
|
log
|- align="center"
| '''Calculation type'''
|
FOPT
|- align="center"
| '''Calculation method'''
|
RB3LYP
|- align="center"
| '''Basis set'''
|
6-31G(d,p)
|- align="center"
| '''Charge'''
|
0
|- align="center"
| '''Spin'''
|
Singlet
|- align="center"
| '''Final energy (a.u.)'''
|
-242.68459891
|- align="center"
| '''RMS Grad Norm (a.u.)'''
|
0.00010587
|- align="center"
| '''Dipole moment'''
|
0.0001 D
|- align="center"
| '''Point group'''
|
C1
|- align="center"
| '''Calculation time'''
|
1m 38 secs
|}

<pre>Item Value Threshold Converged?
Maximum Force 0.000114 0.000450 YES
RMS Force 0.000048 0.000300 YES
Maximum Displacement 0.000558 0.001800 YES
RMS Displacement 0.000206 0.001200 YES
Predicted change in Energy=-3.585769D-07
Optimization completed.
-- Stationary point found.</pre>

<pre>Low frequencies --- -8.7385 -1.2062 -0.0009 -0.0001 0.0002 6.6430
Low frequencies --- 289.5220 289.6665 404.7099</pre>

The optimisation file is linked to [[media:SP_BORAZINE_OPTHIGH.LOG| here]].
The frequency file is linked to [[media:SP_BORAZINE_FREQ.LOG| here]].
{{DOI|10042/26132}}

For borazine, the N-H bond length is 1.01 Å, the B-H bond length is 1.20 Å and each B-N bond length is 1.43 Å. There is variation in the bond angles, from 117 to 123 °.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Type of charge display'''
| width="150" | '''Image'''

|- align="center"
| ''Colour atoms by charge''
|
[[Image:borazine_nbo_colour.png|300px]]
|- align="center"
| ''Show numbers''
|
[[Image:borazine_nbo_numbers.png|300px]]
|}

The charge range is -1.111 to +1.111.

In borazine, there are two types of B-N bonds. The first is 77% B and 23% B, both sp2 orbitals. The second is 88% N and 12% B, this being the one using p orbitals. The H-N bonds are 28% H and 72% N (s and sp3 respectively) and the B-H bonds are 46% B and 54% H (sp2 and s respectively).
The order of bond energies has N-B (non pi) lowest (-0.68) followed by N-H (-0.61), B-H (-0.41) and N-B (pi) (-0.27).

'''Comparing the charge distributions'''

[[Image:charge_comparisons.png|800px]]

{| class="wikitable"
|-
! Benzene atom !! Benzene charge !! Boratabenzene atom !! Boratabenzene charge !! Pyridinium atom !! Pyridinium charge !! Borazine atom !! Borazine charge
|-
| C1 || -0.238 || B1 || +0.202 || N1 || -0.481 || N1 || -1.11
|-
| C2 || -0.238 || C2 || -0.588 || C2 || 0.072 || B2 || 0.754
|-
| C3 || -0.238 || C3 || -0.250 || C3 || -0.242 || N3 || -1.11
|-
| C4 || -0.238 || C4 || -0.340 || C4 || -0.119 || B4 || 0.754
|-
| C5 || -0.238 || C5 || -0.250 || C5 || -0.242 || N5 || -1.11
|-
| C6 || -0.238 || C6 || -0.588 || C6 || 0.072 || B6 || 0.754
|-
| H1 || +0.238 || H1 || -0.097 || H1 || 0.486 || H1 || 0.433
|-
| H2 || +0.238 || H2 || 0.184 || H2 || 0.285 || H2 || -0.077
|-
| H3 || +0.238 || H3 || 0.179 || H3 || 0.297 || H3 || 0.433
|-
| H4 || +0.238 || H4 || 0.186 || H4 || 0.291 || H4 || -0.077
|-
| H5 || +0.238 || H5 || 0.179 || H5 || 0.297 || H5 || 0.433
|-
| H6 || +0.238 || H6 || 0.184 || H6 || 0.285 || H6 || -0.077
|}

The charge distribution in benzene is, unsurprisingly, the simplest of all. Each carbon atom has the same negative charge, -0.238, and each H atom has the same positive charge, equal in magnitude but opposite in sign to that of carbon. This reflects the idea that there is more electron density in the ring itself and that carbon is more electronegative than hydrogen. The range of -0.238 to +0.238 is relatively small compared to the benzene derivatives; the electronegativity difference is not large.

Boratabenzene has a more interesting charge distribution. H is slightly more electronegative than B, hence for the B-H unit, it is H that has the negative charge and B with the positive charge. However, because this electronegativity difference is even smaller than for C and H, the charges on these two atoms are smaller than those in benzene. The carbons adjacent to the B have increased negative charge compared to benzene carbons; they are attached to both a more electropositive H but this time also the even more electropositive B. The next pair of carbon atoms around the ring are again have more negative charge than those in benzene, but reduced compared to the carbons attached to B. However, the carbon para to the boron has more negative charge than the pair next to it. The ring as a whole has a more negative charge than for benzene (-1.814); when the total charge of the H atoms (+0.815) is taken into consideration, this leaves the overall -1 charge of the anion.

In pyridinium, the N-H unit displays the largest charges, due to the high electronegativity of nitrogen. Its H atom has a more or less equal in magnitude but opposite in sign charge. The carbons adjacent to the N display a small positive charge; however, the remaining carbons and hydrogens display similar charge distribution to that of benzene.

Borazine has an overall neutral charge. Each nitrogen has the same, large negative charge and every boron has the same, large (though slightly reduced) positive charge, reflecting the large electronegativity difference between the two atoms. Each boron H and nitrogen H has the same charge with charge signs reflecting that of B/N. The boron H has a very small negative charge, reflecting the much higher electronegativity of the nitrogen atom also attached to each B.

'''Comparing the molecular orbitals'''

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Benzene 7: -0.84624''
|
[[Image:benzene_mo1.png|150px]]
| ''Boratabenzene 7: -0.60393''
|
[[Image:boratabenzene_mo1.png|150px]]
|- align="center"
| ''Benzene 8: -0.73992''
|
[[Image:benzene_mo2.png|150px]]
| ''Boratabenzene 8: -0.51913''
|
[[Image:boratabenzene_mo2.png|150px]]
|- align="center"
| ''Benzene 9: -0.73992''
|
[[Image:benzene_mo3.png|150px]]
| ''Boratabenzene 9: -0.46063''
|
[[Image:boratabenzene_mo3.png|150px]]
|}

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''
| width="150" | '''Molecular orbital'''
| width="150" | '''Image'''

|- align="center"
| ''Pyridinium 7: -1.20934''
|
[[Image:Pyridinium_mo1.png|150px]]
| ''Borazine 7: -0.88193''
|
[[Image:Borazine_mo1.png|150px]]
|- align="center"
| ''Pyridinium 8: -1.02549''
|
[[Image:Pyridinium_mo2.png|150px]]
| ''Borazine 8: -0.83040''
|
[[Image:Borazine_mo2.png|150px]]
|- align="center"
| ''Pyridinium 9: -0.99157''
|
[[Image:Pyridinium_mo3.png|150px]]
| ''Borazine 9: -0.83040''
|
[[Image:Borazine_mo3.png|150px]]
|}

The three molecular orbitals chosen to compare were the three lowest orbitals (not including the core orbitals). For benzene, this orbital of lowest energy is the sigma completely bonding MO. The two MOs above this are degenerate (have the same energy).
For boratabenzene, there is little electron density on the B atom. For pyridinium, the electron density is drawn towards the nitrogen. For the borazine, there is less electron density on the B atoms than the N atoms.
For boratabenzene, each of these three orbitals is of higher energy than its corresponding MO in benzene, telling us that these MOs are less stable in boratabenzene. In addition, MOs 8 and 9 are not degenerate this time.
In pyridinium, the MOs are of the lowest energy yet, and again there is no degeneracy in these orbitals.
For borazine, the MOs are of higher energy than pyridinium, though this time there is again degeneracy in the two higher energy orbitals.

{| border="1" cellpadding="5"
|- align="centre"
| width="150" | '''Molecule'''
| width="150" | '''Energy (A.U.)'''

|- align="center"
| ''Benzene''
|''-232.25820396''
|- align="center"
| ''Boratabenzene''
|''-219.02052295''
|- align="center"
| ''Pyridinium''
|''-248.66806081''
|- align="center"
| ''Borazine''
|''-242.68459891''
|}

This shows that pyridinium is actually the most stable of the molecules, followed by borazine and benzene, with the least stable being boratabenzene.