Rep:Mod:aquila
Sam's Computational Wiki Page Week 2
Investigating Aromaticity
The purpose of this project was to use the tools available through gaussian to study benzene and similar analogues to identify information about their molecular orbitals and charge distribution. Benzene and three analogues; boratabenzene, pyridinium and borazine were investigated in the same way, beginning with an optimisation of their geometry which was followed up with a frequency analysis to confirm that a minima had been found. Then a population analysis was run for each of the optimised structures to generate the molecular orbitals and to allow for NBO analysis to be performed. An MO diagram was constructed for Benzene. All calculations were performed on the HPC
Benzene
Optimisation
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Energy | -232.25820551 a.u. |
| Gradient | 0.00009549 a.u. |
| Dipole Moment | 0.0001 Debye |
| Point Group | C1 |
| Calculation time | 00:02:03:100* |
- Time Format: hh:mm:ss:msmsms
Successful Convergence of Benzene Optimisation
Item Value Threshold Converged? Maximum Force 0.000212 0.000450 YES RMS Force 0.000085 0.000300 YES Maximum Displacement 0.000991 0.001800 YES RMS Displacement 0.000315 0.001200 YES
Link to file for Benzene optimisation on the D-spaceDOI:10042/22884
Frequency Analysis
Link to File published on d-space for frequency analysis of benzene DOI:10042/22885
Results of the Successful Frequency analysis of Benzene are shown below
| File Type | .log |
| Calculation Type | FREQ |
| Basis Set | 6-31G d,p |
| Energy | -232.25820298 |
| Gradient | 0.00009245 |
| Dipole Moment | 0.0001 Debye |
| Point Group | C1 |
| Calculation time | 00:11:23:100 |
Successful convergence of Benzene frequency analysis
Item Value Threshold Converged? Maximum Force 0.000190 0.000450 YES RMS Force 0.000092 0.000300 YES Maximum Displacement 0.000971 0.001800 YES RMS Displacement 0.000372 0.001200 YES
Low frequencies are within acceptible limits and there are no negative frequencies
Low frequencies --- -15.5663 -14.5022 -13.9318 -0.0004 0.0002 0.0003
Low frequencies --- 414.0684 414.1453 620.9624
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A A A
Frequencies -- 414.0683 414.1453 620.9624
Red. masses -- 2.9400 2.9392 6.0697
Frc consts -- 0.2970 0.2970 1.3790
IR Inten -- 0.0000 0.0000 0.0000
It was found that if symmetry of Benzene was restricted to D6h for the frequency analysis, no vibrations would be displayed in the log file. to get around this the symmetry wasn't restricted which had the disadvantage of the symmetry labels of the vibrations not being correct, as C1 symmetry was adopted and only one symmetry label, A, exists for that point group. The vibrations of benzene are listed in the table below.
| Mode no. | Form of Vibration | Frequency | Intensity | Symmetry Label |
|---|---|---|---|---|
| 1 | Symmetric out of plane bending vibration. Carbon atoms at 1 and 4 positions move, in a concerted fashion, back and forth across the plane of the ring | 414.07 | 0.000 | |
| 2 | Asymmetric, out of plane bending vibration. Carbon atoms at 2, 3, 5 and 6 positions move back and forth across the plane of the ring. Atoms 2 and 5 remain on same side of the ring to and atoms 3 and 6 remain on the opposite side | 414.15 | 0.000 | |
| 3 | 620.96 | 0.000 | ||
| 4 | 620.97 | 0.000 | ||
| 5 | Symmetric, out of plane C-H bending. All hydrogen atoms move back and forth across the plane of the ring in a concerted fashion | 693.05 | 74.2466 | |
| 6 | 718.31 | 0.000 | ||
| 7 | 864.10 | 0.000 | ||
| 8 | 864.17 | 0.000 | ||
| 9 | 973.64 | 0.000 | ||
| 10 | 973.73 | 0.000 | ||
| 11 | 1012.37 | 0.000 | ||
| 12 | 1017.88 | 0.000 | ||
| 13 | 1019.95 | 0.000 | ||
| 14 | In plane, C- H symmetric bending vibration. Hydrogen atoms bonded at the 2, 3, 5 ad 6 positions move back and forth in the plane of the ring towards the carbon atoms at the 1 and 4 positions | 1066.34 | 3.3969 | |
| 15 | In plane bending vibration, bond between C2 and C3 and the bond between C5 and C6 relax and contract antagonistically causing a bend in the ring | 1066.43 | 3.3997 | |
| 16 | 1179.25 | 0.000 | ||
| 17 | 1202.17 | 0.000 | ||
| 18 | 1202.28 | 0.000 | ||
| 19 | 1356.09 | 0.000 | ||
| 20 | 1380.24 | 0.000 | ||
| 21 | In plane bending vibration, bond between carbon atoms 2 and 3 and the bond between 5 and 6 remain fixed whilst the 4 bonds can be split in to antagonistic pairs where in the vibration motion one pair is contracting and the other is relaxing. The hydrogen atoms at the 2, 3, 5 and 6 positions move in a concerted fashion towards the pair of carbon bonds that are relaxing | 1524.35 | 6.6222 | |
| 22 | In plane Bending Vibration. Bonds between carbon atoms 2 and 3 and 5 and 6 contract and relax anatgonistically whilst the other CC bonds remain approximately fixed in length. Gives rise to bending of the ring. All hydrogen atoms move towards the carbon-carbon bond that is contracting during the vibration. | 1524.43 | 6.6173 | |
| 23 | 1653.03 | 0.000 | ||
| 24 | 1653.15 | 0.000 | ||
| 25 | Stretching vibration, hydrogen atoms stretch and contract antagonistically. Hydrogen atoms at 1, 3 and 5 positions move in unison and antagonise hydrogen atoms at the 2, 4 and 6 positions. Some slight bending of the ring also occurs | 3174.34 | 0.0013 | |
| 26 | 3183.81 | 0.0001 | ||
| 27 | 3183,99 | 0.0001 | ||
| 28 | Stretching vibration. All six hydrogen atoms undergo stretching and can be grouped in to different categories. Atoms 1, 2 and 6 antagonise atoms 3, 4, and 5. However the bonds to hydrogens atoms 1 and 4 undergo noticebly greater bond stretching and so the speed at which they oscillate is greater than that of the atoms dispite reaching the limits of the stretch/contraction at the same time as the other hydrogen atoms. Some minor ring bending also occurs | 3199.48 | 46.5815 | |
| 29 | Asymmetric Stretching vibration. Hydrogen atoms 2 and 3 antagonise atoms 5 and 6, stretching as the other C-H bonds contract. A minimal amount of stretching is observed for hydrogen atoms 1 and 4 and there is noticeable ring bending. | 3199.65 | 46.5253 | |
| 30 | 3210.15 | 0.0003 |
Population Analysis
Link to file published on D-space for Benzene population Analysis DOI:10042/22905
A population analysis of benzene was then performed on the optimised benzene structure, using the formtatted checkpoint file outputted by the HPC. Before performing the population analysis D6h symmetry was enforced and the keyword "pop=full" was used in setting up the calculation. Natural bond orbital analysis performed using the .log output showed small differences in charge between the carbon and hydrogen atoms, as indicaed in the dark red and green shades used to colour the atoms in the picture right with brighter shades indicated more highly charged atoms. A fixed colour range from -1.00 to 1.00 was used. The specific charges on the atoms were +0.239 on hydrogen and -0.239 on the carbon atoms.
A later test run of the frequency analysis showed that when D6h symmetry was enforced, the frequency analysis fails to produce the desired vibrations
Boratabenzene
Optimisation
Link to published file on D-space for Boratabenzene optimisation DOI:10042/22886
Results for Boratabenzene optimisation
Item Value Threshold Converged? Maximum Force 0.000159 0.000450 YES RMS Force 0.000069 0.000300 YES Maximum Displacement 0.000878 0.001800 YES RMS Displacement 0.000326 0.001200 YES
Convergence successful
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G d,p |
| Energy | -219.02052984 a.u. |
| Gradient | 0.00015840 |
| Dipole Moment | 2.8465 Debye |
| Point Group | C1 |
| Calculation Time | 00:03:58:700 |
Frequency Analysis
Link to published file on D-space for Boratabenzene frequency anaylsis DOI:10042/22882
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G d,p |
| Energy | 219.02052210 a.u. |
| Gradient | 0.00017656 a.u. |
| Dipole Moment | 2.85 Debye |
| Point Group | C2v |
| Calculation Time | 00:05:46:5 |
Item Value Threshold Converged? Maximum Force 0.000437 0.000450 YES RMS Force 0.000157 0.000300 YES Maximum Displacement 0.000854 0.001800 YES RMS Displacement 0.000386 0.001200 YES Predicted change in Energy=-7.082350D-07 Optimization completed. -- Stationary point found.
Frequency Analysis Successfully Converged
Low frequencies --- -6.8690 -0.0007 -0.0004 -0.0003 3.2436 5.5846
Low frequencies --- 371.2620 404.4986 565.1651
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A A A
Frequencies -- 371.2620 404.4985 565.1651
Red. masses -- 2.6899 3.2177 5.7690
Frc consts -- 0.2184 0.3102 1.0857
IR Inten -- 2.2987 0.0000 0.1564
Low frequencies are within acceptable limits and there are no negative frequencies.
Population Analysis
Link to file published on D-space for Boratabenzene population analysis DOI:10042/22808
Pyridinium
Optimisiation
Link to file published to D-space for Pyridinium optimisation DOI:10042/22806
Item Value Threshold Converged? Maximum Force 0.000065 0.000450 YES RMS Force 0.000023 0.000300 YES Maximum Displacement 0.000826 0.001800 YES RMS Displacement 0.000176 0.001200 YES
Convergence Successful
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G d,p |
| Energy | -248.66807396 a.u. |
| Gradient | 0.00003894 a.u. |
| Dipole Moment | 1.8727 Debye |
| Point Group | C1 |
| Calculation Time | 00:04:00:5 |
Frequency Analysis
Link to file published to D-space for Pyridinium frequency analysis DOI:10042/22784
| File Type | .log |
| Calculation Type | FREQ |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G d,p |
| Energy | -248.66806065 a.u. |
| Gradient | 0.00008670 |
| Dipole Moment | 1.8719 Debye |
| Point Group | C2v |
| Calculation time | 00:05:38:5 |
Item Value Threshold Converged? Maximum Force 0.000242 0.000450 YES RMS Force 0.000087 0.000300 YES Maximum Displacement 0.001176 0.001800 YES RMS Displacement 0.000387 0.001200 YES
Frequency Analysis Convergence Successful
Low frequencies --- -10.6391 -9.6790 0.0007 0.0010 0.0011 9.8078
Low frequencies --- 392.1034 404.1191 620.2636
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
B1 A2 A1
Frequencies -- 392.1034 404.1191 620.2636
Red. masses -- 2.9456 2.7465 6.2546
Frc consts -- 0.2668 0.2643 1.4178
IR Inten -- 0.9913 0.0000 0.0145
Low frequencies within acceptable limits and there are no negative frequencies
Population Analysis
Link to file published to D-space for Pyridinium population analysis DOI:10042/22804
Borazine
Optimisation
Link to file on D-space for Borazine Optimisation DOI:10042/22783
Item Value Threshold Converged? Maximum Force 0.000057 0.000450 YES RMS Force 0.000017 0.000300 YES Maximum Displacement 0.000748 0.001800 YES RMS Displacement 0.000201 0.001200 YES
Successful Convergence
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G d,p |
| Energy | -242.68458998 a.u. |
| Gradient | 0.00002129 a.u. |
| Dipole Moment | 0.0006 Dipole |
| Point Group | C1 |
| Calculation time | 00:11:15:5 |
Frequency Analysis
Link to file published on D-space for frequency analysis of Borazine DOI:10042/22782
| File Type | .log |
| Calculation Type | FREQ |
| Calculation Method | RB3LYP |
| Basis Set | 6-31G d,p |
| Energy | -242.68459825 a.u. |
| Gradient | 0.00001386 a.u. |
| Dipole Moment | 0.0006 |
| Point Group | C1 |
| Calculation Time | 00:11:25:3 |
Item Value Threshold Converged? Maximum Force 0.000036 0.000450 YES RMS Force 0.000014 0.000300 YES Maximum Displacement 0.000648 0.001800 YES RMS Displacement 0.000251 0.001200 YES
Low frequencies --- -7.3827 -6.4681 -5.8389 -0.0009 -0.0006 0.0005
Low frequencies --- 289.4766 289.6115 404.4214
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A A A
Frequencies -- 289.4766 289.6114 404.4214
Red. masses -- 2.9270 2.9269 1.9273
Frc consts -- 0.1445 0.1446 0.1857
IR Inten -- 0.0000 0.0000 23.5969
Low Frequencies are within acceptable limits and no negative frequencies were observed
Population Analysis
Link to file published to D-space for population analysis of Borazine DOI:10042/22881
Comparison of Molecular Orbitals
| Benzene | Boratabenzene | Pyridinium | Borazine | |
|---|---|---|---|---|
| Structures |  |
 |
 |
 |
| Orbital 16 |  |
 |
 |
 |
| Comments | carbon atoms at 1 and 4 positions do not contribute to the orbital, no electron density covers the ipso and para hydrogens | Lobe overlaps the ortho and ipso hydrogens and lobe of opposite phase on the para hydrogen. Leaving the meta hydrogens with no electron density surrounding them. Result is a less symmetric orbital when compared with benzene orbital 16 | For pyridinium the nitrogen atom doesn't contribute any electron density but the orbital lobes appear distorterd in comparison with benzene. The central red and green lobes don't extend as far across the ring and the lobes surrounding them extend further, coming in to close contact at the number 4 carbon | A drastically different orbital is observed for borazine at the 16th level. σ p-s type bonding is observed between boron atoms and their bound hydrogen. Where as the nitrogen atoms appear to only undergo s-s type σ bonding, and the orbitals involving nitrogen are markedly more contracted than those oberved for boron atoms |
| Orbital 19 |  |
 |
 |
 |
| Comments | Shows close similarity with orbital 18 of Benzene that has degeneracy with orbital 19. However in benzene there are nodes in between orbital lobes that are not observed for Boratabenzene | Close comparison to orbital 19 of benzene, noticeable differences are that the lobe encompassing the ipso hydrogen is more contracted than in benzene and the lobe encompassing the para hydrogen is more diffuse in comparison with benzene | Comparible with orbital 19 of boratabenzene in terms of shape. Lobes surrounding the ortho hydrogen atoms are considerably large in borazine and the size of the lobes surrounding the meta hydrogens is lessened | |
| Orbital 21 |  |
 |
 |
 |
| Comments | Different lobes of the π system are equal in size | The presence of the boron atom appears to have made the lobe of the molecular orbital it contributes to more diffuse | For pyridinium the no 21 orbital is similar in shape as the degenerate orbital no 20 for benzene. The nitrogen atom does not contribute to this orbital so there is no distortion of the orbital lobes | For borazine, the lobes covering the single nitrogen atom and two boron atoms is noticeably smaller than the lobes covering the two nitrogen atoms and single boron atom |
Natural Bonding Orbital Analysis
The combined population analyses allowed for a comparison of the charge distribution on the atoms at each position of the benzene analogues and therefore determine the influence of the substituted atoms.
| Benzene | Boratabenzene | Pyridinium | Borazine | |
|---|---|---|---|---|
| Molecule image | |
|
|
|
| Charge distribution (red = negative, green = positive. light shades = high charge) | ||||
| Numbered charge structures | ||||
| Values | C1: -0.239, C2: -0.239, C3: -0.239, C4: -0.239, C5: -0.239, C6: -0.239. H1: +0.239, H2: +0.239, H3: +0.239, H4: +0.239, H5: +0.239, H6: +0.239. | B1: +0.202, C2: -0.588, C3:-0.250, C4:-0.340, C5:-0.250, C6:-0.588. H1:-0.095, H2:+0.184, H3:+0.179, H4:+0.186, H5:+0.179, H6:+0.184. | N1: -0.476, C2: +0.071, C3: -0.241, C4:-0.122, C5:-0.241, C6:+0.071. H1:+0.483. H2+0.285, H3:+0.297, H4:+0.292, H5:+0.297, H6:+0.285. | N1: -1.102, B2:+0.747, N3:-1.102, B4:+0.747, N5:-1.102, B6:+0.747. H1:+0.432, H2:-0.077, H3:+0.432, H4:-0.077, H5:+0.432, H6:-0.077 |
Interpretation of Charge Data
Due to the high level of symmetry in benzene the charges across all the carbon atoms are the same, -0.239, and the same across all the hydrogen atoms, +0.239, giving a total charge of 0 as is expected for a typically neutral molecule. Benzene will be used as a reference in describing the influence of the different elements substituted in to the ring in the Benzene analogues
In boratabenzene the presence of the boron atom increases the electron density of all the carbon atoms and hydrogen atoms in the molecule, relative to benzene. Charge is localised most on the carbon atoms at the 2, 6 positions, with the effective charge (-0.588), over double that seen for the carbon atoms in benzene. Carbon atom at the 4 position also has a significantly greater electron density, with a charge of -0.340, than that observed in benzene. This can be account for by boron's lower electronegativity than carbon and so electron density on boron can be easily drawn away by the carbon atoms through the π-bonding system. The explanation as to why the carbon atoms at the 2,4 and 6 positions can be shown through resonance. See image below
Hydrogen also has a greater electronegativity than boron and so likely draws some electron density from the ring through an inductive effect, as the positive charge on the hydrogen atoms bound to carbon atoms is lessened, in comparison to benzene.
The optimised structure of boratabenzene shows that there is no π delocalisation over the boron atom. The significant negative charge over all the carbon atoms, equivalent to two formal negative charges, in the ring might suggest that there is very little π electron density between the boron atoms and adjacent carbon atoms. The carbon atoms draw so much of the electron density, by nature of having greater electronegativity, from the boron atom that there is insufficient electron density for any strong п-bonding interaction, hence why there is no delocalisation of the π system over the boron atom.
For Pydridinium, the nitrogen atom has the opposite effect of boron in boratabenzene. The nitrogen atom withdraws electron density from the ring due to its greater electronegativity than carbon. The carbon atoms at the 2,4 and 6 positions experience a noticeable increase in positive charge with the carbon atoms adjacent to the nitrogen experiencing the greatest loss of electron density with charges of +0.071. Surprisingly the carbon atoms at the 3 and 5 positions have a marginally higher negative charge, than in benzene, of -0.241. The hydrogen atoms experience an increase in positive charge, but not as great as the carbon atoms. An explanation of charges can be shown through resonance structures, see image below. The hydrogen atom bonded directly to the nitrogen atom experiences a large increase in positive charge, as would be expected.
Unlike boratabenzene, pyridinium shows complete delocalisation around the entire ring. This might be due to the heteroatom being more electronegative than the carbon atoms in the ring in this case and so the carbon atoms are unable to draw π electron density away from the heteroatom. There is significant electron density located at the nitrogen but with its electronegativity and carbon's being close, electrons from nitrogen are likely to delocalised in the ring to some extent, creating an aromatic structure.
In borazine the nitrogen atoms are bonded to atoms that are all less electronegative than they are, so they experience a very large increase in electron density greater than a single formal negative charge (-1.102). The boron atoms are surrounded by atoms that are all more electronegative than it and so experiences a very large loss in electron density. However the electronegativities of hydrogen and boron are quite close, so the increase in charge is not as great in magnitude as that the charge obtained by the nitrogen atoms.
Despite being labelled 'inorganic benzene' the optimised borazine strucure shows no delocalisation, despite being isoelectronic with benzene, having the same number of π electrons and uniform bond lengths for all N-B bonds. This might be because the π electrons are located on the nitrogen atoms and delocalisation of these electrons would involve donation of these electrons to form the π bonds. This would be energetically unfavourable considering the large difference in electronegativity between nitrogen and boron, the nitrogen atoms would be reluctant to lose electron density and attain a positive charge in order to achieve aromaticity. The stabilisation energy obtained from aromaticity would likely be outweighed by the destabilisation resulting from the negative charge on the boron atoms and the positive charge on the nitrogen atoms. It would be more likely that the most electronic structure is for electron density remain on the nitrogen atoms, as is evident from the charge distribution data.