ChemWiki - User contributions [en]

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:32:04Z

Js3311: /* Effect of functional groups on HOMO and LUMO */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

Another observation would be that the larger the contribution of the heteroatom to the C-X bond, the more negative the heteroatom is in the charge distribution. It can be seen that when X = N, the contribution by N to the bond is 66 %, and the charge distribution has a negative value of -0.295. However as the contribution of X dropped to 40 % as with P, the charge distribution value is now positive at 1.667.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 11:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:31:37Z

Js3311: /* Effect of functional groups on charge distribution */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

Another observation would be that the larger the contribution of the heteroatom to the C-X bond, the more negative the heteroatom is in the charge distribution. It can be seen that when X = N, the contribution by N to the bond is 66 %, and the charge distribution has a negative value of -0.295. However as the contribution of X dropped to 40 % as with P, the charge distribution value is now positive at 1.667.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:31:15Z

Js3311: /* Optimisation and frequency analysis */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

Another observation would be that the larger the contribution of the heteroatom to the C-X bond, the more negative the heteroatom is in the charge distribution. It can be seen that when X = N, the contribution by N to the bond is 66 %, and the charge distribution has a negative value of -0.295. However as the contribution of X dropped to 40 % as with P, the charge distribution value is now positive at 1.667.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:30:57Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

Another observation would be that the larger the contribution of the heteroatom to the C-X bond, the more negative the heteroatom is in the charge distribution. It can be seen that when X = N, the contribution by N to the bond is 66 %, and the charge distribution has a negative value of -0.295. However as the contribution of X dropped to 40 % as with P, the charge distribution value is now positive at 1.667.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:18:17Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

Another observation would be that the larger the contribution of the heteroatom to the C-X bond, the more negative the heteroatom is in the charge distribution. It can be seen that when X = N, the contribution by N to the bond is 66 %, and the charge distribution has a negative value of -0.295. However as the contribution of X dropped to 40 % as with P, the charge distribution value is now positive at 1.667.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:08:01Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T13:06:05Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

In addition, from the population analysis, it is possible to understand the nature of the C-X bond, where X is the central heteroatom. The contribution of the each atom to the C-X bond can be found in the .log of the population analysis. Here it is tabulated and shown in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

One significant observation would be that this result coincides with the understanding of the electronegativity of the elements involved (C, N, P and S). The electronegativity is given by the order N > S > C > P, where S and C have very marginal difference and can be regarded to have almost the same electronegativity. When looking at the percentage contribution by each atom, it would agree with the electronegativity of the elements; N has a higher contribution to the electron density in the C-N bond, whereas C has a higher contribution to the electron density in the C-P bond, and there are almost equal contribution by S and C to the C-S bond although a marginally higher contribution by S.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T12:01:00Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T11:43:55Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T11:43:36Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Contribution by C || 34 % || 60 % || 49 %
|-
| Contribution by X || 66 % || 40 % || 51 %
|}

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T11:39:41Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| cell || cell
|-
| cell || cell
|}

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T11:38:47Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Contribution by each atom to the C-X bond
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| cell || cell
|-
| cell || cell
|}

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:24:58Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table 6 it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:24:29Z

Js3311: /* Effect of functional groups on HOMO and LUMO */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 10:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:24:14Z

Js3311: /* Effect of functional groups on charge distribution */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table 9:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:23:53Z

Js3311: /* Optimisation and frequency analysis */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 8:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:23:34Z

Js3311: /* NBO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:23:20Z

Js3311: /* MO Discussion */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table 5:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:22:59Z

Js3311: /* Optimisation and frequency analysis */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables 1, 2 and 3 show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 1:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 2:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table 3:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table 4:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:21:58Z

Js3311: /* Effect of functional groups on HOMO and LUMO */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables XXX, XXX and XXX show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+. This time it makes the cation a better electron acceptor rather than a donor.

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-07T00:17:37Z

Js3311: /* Effect of functional groups on HOMO and LUMO */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables XXX, XXX and XXX show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions). From the relative energies of the HOMO and LUMO of both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ against N(CH3)4+, it is possible to predict the difference in reactivity when altering the functional groups on the cation. When looking at [N(CH3)3(CH2OH)]+, the HOMO increased in energy relative to N(CH3)4+, allowing the cation to be a better electron donor as it would have a better HOMO-LUMO match with the reactant (especially for intramolecular reactions) as given by the Klopman-Salem equation. Similarly when looking at [N(CH3)3(CH2CN)]+, the LUMO energy level dropped relative to N(CH3)4+

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-06T23:54:08Z

Js3311: /* Effect of functional groups on HOMO and LUMO */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables XXX, XXX and XXX show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

Ions are hard molecules as they engage in ionic interactions via electrostatic forces. However, organic cations are large and hence results in a dispersion of charge throughout the whole molecule, This makes the molecule softer and the nature of bonding is governed by HOMO-LUMO interactions (ie. covalent interactions).

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcomp

2014-03-06T23:20:33Z

Js3311: /* Molecular orbital of BH3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table 11. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 11:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table 12:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table 13).

{| class="wikitable" border="1"
|+ '''Table 13:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table 14:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them. This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 15:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 16:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:19:07Z

Js3311: /* Optimisation and frequency analysis */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table 11. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 11:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table 12:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table 13).

{| class="wikitable" border="1"
|+ '''Table 13:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table 14:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 15:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 16:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:18:33Z

Js3311: /* Optimisation and frequency analysis */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table 11. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 11:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table 12:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table 13).

{| class="wikitable" border="1"
|+ '''Table 13:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table 14:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 15:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:18:13Z

Js3311: /* Molecular orbital of BH3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table 11. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 11:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table 12:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table 13).

{| class="wikitable" border="1"
|+ '''Table 13:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table 14:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:17:56Z

Js3311: /* Comparison of results between BH3 and GaBr3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table 11. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 11:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table 12:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table 13).

{| class="wikitable" border="1"
|+ '''Table 13:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:16:38Z

Js3311: /* GaBr3 Frequency analysis */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table 11. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table 11:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table 12:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:15:26Z

Js3311: /* BH3 Frequency analysis */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table 9:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table 10.

{| class="wikitable" border="1"
|+ '''Table 10:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table 10, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table 10). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:14:34Z

Js3311: /* Structural analysis of various compounds */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table 8:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:14:18Z

Js3311: /* A combination of both basis sets and pseudo-potentials */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 6:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 7:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:14:01Z

Js3311: /* Using pseudo-potentials for larger molecules */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table 4:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table 5:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:13:41Z

Js3311: /* Calculations involving basis sets */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table 1.

{| class="wikitable" border="1"
|+ '''Table 1:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table 2:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table 3.

{| class="wikitable" border="1"
|+ '''Table 3:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:13:07Z

Js3311: /* Molecular orbital of BH3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure 3:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:12:48Z

Js3311: /* GaBr3 Frequency analysis */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure 2:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:12:28Z

Js3311: /* BH3 Frequency analysis */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. 1).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure 1:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:11:56Z

Js3311: /* Charge distribution of NH3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. 4).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure 4:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T23:04:47Z

Js3311: /* Comparison of results between BH3 and GaBr3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

When a molecule is being optimised, the method used provides the type of approximation made in solving the Schrodinger equation. The basis set would then provide the degree of accuracy for which this approximation is made. The optimisation would then be carried out whereby the energy and electron density is calculated for every possible position of the nuclei until the lowest possible energy is achieved (ie. a potential energy surface is generated). What the frequency analysis does next would be to calculate the curvature of the potential energy surface to determine if it is a minimum or maximum. Thus the frequency analysis is the second derivative of the function. If the result of the analysis is negative, we have a transition state and if it is positive, it is a minimum. Therefore it is necessary for the optimisation and frequency analysis to use the same method and basis set as the frequency analysis works on the potential energy surface generated by the optimisation step. Using a different method and basis set for the frequency analysis is akin to getting the second derivative of a completely different function and thus lead to an inaccurate result.

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T22:29:53Z

Js3311: /* Association energy of NH3BH3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T22:29:39Z

Js3311: /* Association energy of NH3BH3 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

[[must always remember to talk abt relative energies and not absolute energies]]

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T22:28:13Z

Js3311: /* References */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond[[(cite atkins 932)]] which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

[[must always remember to talk abt relative energies and not absolute energies]]

==References==
<references/>

Rep:Mod:js3311inorgcomp

2014-03-06T22:28:00Z

Js3311: /* References */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond[[(cite atkins 932)]] which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

[[must always remember to talk abt relative energies and not absolute energies]]

==References==
<reference/>

Rep:Mod:js3311inorgcomp

2014-03-06T22:27:41Z

Js3311: /* References */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond[[(cite atkins 932)]] which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

[[must always remember to talk abt relative energies and not absolute energies]]

==References==
</reference>

Rep:Mod:js3311inorgcomp

2014-03-06T22:27:21Z

Js3311: /* Using pseudo-potentials for larger molecules */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å<ref>CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC Press, Boca Raton, 87th edn., 2006.</ref>. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond[[(cite atkins 932)]] which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

[[must always remember to talk abt relative energies and not absolute energies]]

==References==

Rep:Mod:js3311inorgcomp

2014-03-06T22:18:59Z

Js3311: /* Year 3 Inorganic Computational Part 1 */

==Year 3 Inorganic Computational Part 1==
The first part of the inorganic computational assignment involved exploring various functions in GaussView and understanding the background theories behind the various calculations involving different types of basis sets. Different molecules were chosen to illustrate these features including BH3, GaBr3 and BBr3. This was then taken a step further by exploring various types of calculations and then with a better understanding, the same type of calculation was carried out on NH3 and finally the NH3BH3 adduct, of which the association energy of the molecules was derived. After an introduction to these basic calculations, a mini project was carried out on ionic liquid molecules which can be found [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:js3311inorgcompminiproj here].

===Calculations involving basis sets===
Investigation into the optimisation of BH3 was carried out. GaussView was used to build the molecule and calculations were run with the 3-21G basis set on Gaussian. Results of the calculation were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION.LOG|Results of BH3 optimisation 1]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -26.46226429
|-
| Gradient || 0.00008851
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 21.0 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
</pre>
|}

However, the 3-21G basis set is a very simple basis set. A better basis set would be the 6-31G(d,p) basis set, which gives a more accurate calculations closer to observed results. Having optimised the structure using the 3-21G basis set, the 6-31G(d,p) was thus used to further optimise the structure. The results of the calculation was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [[Media:JXS_BH3_OPTIMISATION_631G.LOG|Results of BH3 optimisation 2]]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532360
|-
| Gradient || 0.00000706
|-
| Dipole Moment (Debye) || 0.0001
|-
| Point Group || Cs
|-
| Calculation time taken || 6.0 s
|-
| colspan="2" |
<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=-1.068574D-09
Optimization completed.
</pre>
|}

Following the two calculations, the individual bond lengths and bond angles were tabulated in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BH3
! colspan="4" align="center" | [[File:BH3_321g_labels.jpg|150px]] BH3 optimised with 3-21G basis set !! colspan="4" align="center" | [[File:BH3_631g_labels.jpg|150px]] BH3 optimised with 6-31G(d,p) basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°) !! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-H2 || 1.19 || H2-B1-H3 || 120.0 || B1-H2 || 1.19 || H2-B1-H3 || 120.0
|-
| B1-H3 || 1.19 || H2-B1-H4 || 120.0 || B1-H3 || 1.19 || H2-B1-H4 || 120.0
|-
| B1-H4 || 1.19 || H3-B1-H4 || 120.0 || B1-H4 || 1.19 || H3-B1-H4 || 120.0
|}

It is to note that even though the calculated bond distances and angles are similar to 2 decimal places (or 1 decimal place for bond angles), the values differ slightly at higher accuracy. In general, the bond lengths for BH3 calculated using the 3-21G basis set are longer than that calculated using the 6-31G(d,p) basis set. In addition, the bond angles deviate greater from the average value of 120 ° for the BH3 molecule optimised using the 3-21G basis set (see both .log for exact calculated values). This would therefore illustrate that the 6-31G(d,p) basis set would give more accurate results than the 3-21G basis set.

===Using pseudo-potentials for larger molecules===
The calculation of properties using basis sets has its limitations for larger atoms with more electrons. Larger basis sets can be used but it is an expensive way for calculating these properties. One other alternative would be to use pseudo-potentials which considers only the valence electrons of the heavy atom and approximate the rest of the electrons by treating it as a single function. Here in this section, the use of pseudo-potential is being explored with the molecule GaBr3. The molecule was built on GaussView and optimised using the LanL2DZ pseudo-potential via the High Performance Computer (HPC) on the college server. The results were summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27889 Results of GaBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000016
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 27.8 s
|-
| colspan="2" | <pre> Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282691D-12
Optimization completed.</pre>
|}

Following the calculations, the bond length and bond angles obtained were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of GaBr3
! colspan="4" align="center" | [[File:GaBr3_labels.jpg|150px]] GaBr3 optimised with LanL2DZ pseudo-potential
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| Ga1-Br2 || 2.35 || Br2-Ga1-Br3 || 120.0
|-
| Ga1-Br3 || 2.35 || Br2-Ga1-Br4 || 120.0
|-
| Ga1-Br4 || 2.35 || Br3-Ga1-Br4 || 120.0
|}

The literature reported bond length of Ga-Br is 2.3525 Å{{cn}}. This shows that the computed value does not deviate significantly from the literature value and is in fact close in agreement. The bond angle was computed to be exactly 120.0 ° as the symmetry is restricted to a D3h symmetry and hence would adopt a bond angle of 120.0 °. Therefore this showed that the use of approximate calculations involving pseudo-potentials will still be able to give an accurate estimate of basic properties of large molecules.

===A combination of both basis sets and pseudo-potentials===
Whilst the use of basis set gives a reasonably accurate result on molecules with small atoms and the pseudo-potential gives a good estimation of calculations of molecules with larger, heavier atoms, the combination of basis set and pseudo-potential calculation can be carried out on one molecule with a mixture of both small and large atoms. In the case of BBr3, a 6-31G(d,p) calculation can be carried out on the B atom where as a LanL2DZ pseudo-potential calculation can be carried out on the heavier Br atoms. It was similarly built on GaussView and sent for calculation on the HPC with the basis sets and pseudo-potential specified. The results were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27891 Results of BBr3 optimisation]
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Basis Set || Gen
|-
| Final Energy (au) || -64.43644904
|-
| Gradient || 0.00000962
|-
| Dipole Moment (Debye) || 0.0003
|-
| Point Group || Cs
|-
| Calculation time taken || 39.4 s
|-
| colspan="2" |
<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000107 0.001800 YES
RMS Displacement 0.000062 0.001200 YES
Predicted change in Energy=-2.170128D-09
Optimization completed.
</pre>
|}

The following bond distance and angles from the optimised structures were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Table of bond distances and bond angle of BBr3
! colspan="4" align="center" | [[File:BBr3_labels.jpg|150px]] BBr3 optimised with Gen basis set
|-
! Bond !! Distance (Å) !! Bond Angle !! Value (°)
|-
| B1-Br2 || 1.93 || Br2-B1-Br3 || 120.0
|-
| B1-Br3 || 1.93 || Br2-B1-Br4 || 120.0
|-
| B1-Br4 || 1.93 || Br3-B1-Br4 || 120.0
|}

===Structural analysis of various compounds===
From the above sections, the average computed bond lengths of various bonds is summarised below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Computed average bond length
! Bond !! Bond length (Å)
|-
| B-H || 1.19
|-
| Ga-Br || 2.35
|-
| B-Br || 1.93
|}

When comparing the bond lengths of B-H and B-Br, the effects of changing the ligands can be observed. When the ligand was changed from H to Br, the bond length lengthened from 1.19 Å to 1.93 Å. This can be attributed to the fact that Br is a much larger atom than H, as such the valence orbitals of Br are much more diffuse and further from the nucleus in the 4th quantum shall, leading to a longer bond formed between B and Br. H however, has only 1 electron in the first quantum shell and hence the bond length is shorter as the valence electron is closer to the nucleus. In addition, some of the other differences include the atomic mass of the two atoms, where H has an atomic mass unit of 1 but that of Br is 79.9.

The electronegativity of the two elements also differ. Br is more electronegative than H. This will lead to difference in the dipole moments when bonded with B. A B-H bond has a smaller electronegativity difference between B and H whereas B-Br have a larger electronegativity difference between the two elements. As a result the B-Br has a larger dipole moment than a B-H bond. Also, while H only has 1 valence electron, Br has 7 valence electrons. However, it is to note that both H and Br form a single bond with B as they only require 1 electron to achieve the stable electronic configuration. In addition, the resultant polarity of the two molecule are the same as they adopt a D3h symmetry and thus all the dipole moments within the molecule will cancel out despite B-H and B-Br having different dipole moments.

By comparing the bond lengths of Ga-Br and B-Br, it is also apparent that when changing to a larger central atom, the bond length increases as well. The Ga-Br bond is longer than the B-Br bond (2.35 Å as compared to 1.93 Å) as Ga is larger than B. The same argument which accounted for the increase in bond length when the ligands changed from H to Br can be applied for the central atom as well; bond length increased as the central atom was changed from B to Ga because Ga is a larger atom with its valence shell further away from the nucleus. As bonding occurs at the valence shell, having a quantum shell further away from the nucleus (for Ga) would lead to a longer bond length. While B is on the 2nd period of the periodic table, Ga is on the 4th period of the periodic table. As a result, Ga is much heavier and larger than B. While both elements belong to Group 13, as with the ligands, the electronegativity of the two elements also differ. As Ga is in the 4th period of the periodic table, it has a lower electronegativity compared to B, which will thus affect the individual dipole moments when bonded with Br. The B-Br bond has a lower electronegative difference between the atoms than that of the Ga-Br bond.

In GaussView where the molecules are built, sometimes the bonds does not show even when a bond between two atoms is expected. This is merely because the bond length exceeds a certain pre-defined value in the software and hence it does not draw a line between the two atoms to connect it as a bond. The bond in the software simply conveys a message to users that there is a covalent interaction between the two atoms at the given distance, beyond the pre-defined distance, the software might not recognise it as a covalent interaction, but it does not mean in reality that there is no bond or interaction.

A bond is a force that brings two atoms together. However, a bond is not always depicted by a line. Conventionally, the line that connects the two atoms together is defined to be a covalent bond; a line between the two atoms signify that one electron from each atom is shared in the bonding of the two atoms connected by the line. GaussView might have defined the bond (by means of drawing a line between the two atoms) to be a covalent bond. However there are in fact various types of bonds that exists. Of which only a covalent bond is represented by a line connecting the two atoms. One example of a bond that cannot be represented by a line would be the metallic bond within a metal (eg. Cu). The metallic bonding within a metal is defined to be an array of cationic metal amongst a sea of electrons. Drawing a line between the electron and the cationic metal would not accurately represent the metallic bonding as the line is defined to be a covalent bond where electrons are shared between two atoms, and an electron is not an atom.

There are other forms of bonding as well such as ionic bond, defined as the electrostatic forces between two oppositely charged ions. This bond involves the complete transfer of electrons from one atom to another and no sharing is involved, hence it is also not an accurate depiction by drawing a line between the two ions. Another type of bond would be hydrogen bonding. As hydrogen bonding occurs between a hydrogen directly bonded to a highly electronegative atom (N, O or F) and an electronegative atom, it is a weak interaction where the strength of the bond lies in between a covalent bond and van der Waals forces of attraction. As such, drawing a solid line to indicate such attractive force is not accurate. In fact, it is often depicted by a dotted line to show that it is a weaker form of interaction than covalent bond.

==Year 3 Inorganic Computational Part 2==
With the ability to perform basic optimisation on various types of molecules with the use of various basis sets and also the ability to find out basic properties of the molecules such as bond lengths and bond angles, more complex calculations can be done.

===Frequency analysis===
In this section, frequency analysis was carried on different molecules by means of a frequency calculation on Gaussian. A simulated IR spectrum of the computed molecule can also be generated. Similar to previous section, frequency analysis were carried out on various compounds and were compared against each other.

====BH3 Frequency analysis====
A frequency analysis was first done on the BH3 molecule. The molecule was reoptimised by confining it to the D3h symmetry to provide low frequency values that are closer to the tolerance range of 0 ± 15 cm-1. The molecule was built on GaussView and both the optimisation and the frequency analysis was done using the 6-31G(d,p) basis set, with calculations performed on Gaussian. The table below is a summary of the calculations, together with the required excerpts from the .log files.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of BH3 optimisation and frequency calculation
! !! [[Media:JXS_BH3_OPTIMISATION_631G_2.LOG|Optimisation]] !! [[Media:JXS_BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363 || -26.61532363
|-
| Gradient || 0.00000296 || 0.00000291
|-
| Dipole Moment (Debye) || 0.0000 || 0.0000
|-
| Point Group || D3h || D3h
|-
| Calculation time taken || 5.0 s || 6.0 s
|-
| || <pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.996524D-10
Optimization completed.</pre>
|}

Following the frequency analysis, the different vibrational modes of the molecule were tabulated and summarised in Table XXX.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of BH3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| 1163 || 93 || A2"
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| 1213 || 14 || E'
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Rocking motion of 2 B-H bonds in the plane of the molecule and another B-H bond bending in the opposite direction of the rocking motion (bending motion)|| 1213 || 14 || E'
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| 2582 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| 2715 || 126 || E'
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| 2715 || 126 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.9432 -0.8611 -0.0054 5.7455 11.7246 11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853
</pre>
|}

From here, it can be seen that there are 6 different vibrational modes for BH3. This would correspond to the theory that a molecule would have 3N-6 vibrational modes for a non-linear molecule and 3N-5 vibrational modes for linear molecules, where N is the number of atoms in the molecule. Here for BH3, N=4 and therefore would work out to have 6 vibrational modes which agrees with the Gaussian-computed results. A computed IR spectrum was also generated (Fig. XXX).

[[File:JXS_predicted_IR_spectrum.jpg|600px]]
 '''Figure XXX:''' Simulated IR spectrum of BH3

From Table XXX, it shows that there are 6 vibrational modes. However from the IR spectrum, only 3 different peaks were observed. This is due to 2 factors, the first being that the vibrational frequency at 2582 cm-1 is not IR active and hence does not show up on the IR spectrum. IR spectroscopy only captures vibrational mode that have a resultant dipole moment. Due to the symmetrical stretching of the B-H bonds, the dipole moments cancel out each other and hence the resultant dipole moment is zero (as illustrated by the zero intensity on Table XXX). Therefore this peak is not observed.

Another reason would be due to degeneracy in the vibrational modes. As shown in the table, there are two vibrational modes with the same frequency at 1213 cm-1 and another two at 2715 cm-1. Therefore only 2 peaks reflect the 4 vibrational modes mentioned and hence, reducing the number of peaks observed on the spectrum.

====GaBr3 Frequency analysis====
A similar frequency analysis was carried out for the GaBr3 molecule. With the molecule already optimised as a D3h molecule, a frequency calculation was done via the HPC and the different vibrational modes tabulated below in Table XXX. The same LanL2DZ basis set used to optimise the molecule was used to carry out the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27892 Results of GaBr3 frequency calculation]
|-
| File Type || .log
|-
| Calculation Type || Freq
|-
| Basis Set || LanL2DZ
|-
| Final Energy (au) || -41.70082783
|-
| Gradient || 0.00000011
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 16.8 s
|-
| colspan="2" | <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=-6.142862D-13
Optimization completed.
</pre>
|}

The different vibrational modes were also tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Different Vibrational Modes of GaBr3
! No. !! Type of vibration !! Frequency (cm-1) !! Intensity !! Point Group
|-
| 1 || align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 2 || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| 76 || 3 || E'
|-
| 3 || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| 100 || 9 || A2"
|-
| 4 || align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| 197 || 0 || A1'
|-
| 5 || align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| 6 || align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| 316 || 57 || E'
|-
| colspan="5" |
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>
|}

As both BH3 and GaBr3 have the same number of atoms and have the same shape, it is clear that there are also 6 vibrational modes for GaBr3. In addition, the simulated IR spectrum is also generated in the following figure.

[[File:JXS_predicted_IR_spectrum_GaBr3.jpg|600px]]
 '''Figure XXX:''' Simulated IR Spectrum of GaBr3

Again, the simulated spectrum only shows 3 peaks for 6 vibrational modes. This is due to the same reasons as mentioned above for BH3, where the symmetrical stretch of Ga-Br bonds (No. 4) is not active by IR spectroscopy and there are 2 degenerate pairs of vibrational modes (No. 1/2 and No. 5/6).

====Comparison of results between BH3 and GaBr3====
A comparison of the vibrational modes of the two molecules can also be made. A comparison table was done and summarised below (Table XXX).

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of Vibrational Modes between BH3 and GaBr3
! !! colspan="2" align="center" | BH3 !! colspan="2" align="center" | GaBr3
|-
! No. !! Type of vibration !! Frequency (cm-1) (Intensity) !! Type of vibration !! Frequency (cm-1) (Intensity)
|-
| 1 || align="center" | [[File:JXS_BH3_1_freq.gif|150px]] Wagging of all 3 B-H bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 1163 (93)|| align="center" | [[File:JXS_GaBr3_1_freq.gif|150px]] Bending motion of a Ga-Br bond in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 2 || align="center" | [[File:JXS_BH3_2_freq.gif|150px]] Scissoring motion of 2 B-H bonds in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_2_freq.gif|150px]] Scissoring motion of 2 Ga-Br bonds in the plane of the molecule (bending motion)|| align="center" | 76 (3)
|-
| 3 || align="center" | [[File:JXS_BH3_3_freq.gif|150px]] Bending motion of a B-H bond in the plane of the molecule (bending motion)|| align="center" | 1213 (14) || align="center" | [[File:JXS_GaBr3_3_freq.gif|150px]] Wagging of all 3 Ga-Br bonds perpendicular to the plane of the molecule (bending motion)|| align="center" | 100 (9)
|-
| 4 || align="center" | [[File:JXS_BH3_4_freq.gif|150px]] Symmetrical stretching of all 3 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2582 (0)|| align="center" | [[File:JXS_GaBr3_4_freq.gif|150px]] Symmetrical stretching of all 3 Ga-Br bonds in the plane of the molecule (stretching motion)|| align="center" | 197 (0)
|-
| 5 || align="center" | [[File:JXS_BH3_5_freq.gif|150px]] Asymmetrical stretching of 2 B-H bonds in the plane of the molecule (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_5_freq.gif|150px]] Asymmetrical stretching of 2 Ga-Br bonds in the plane of the molecule with simultaneous bending motion of the other Ga-Br bond also in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (5)
|-
| 6 || align="center" | [[File:JXS_BH3_6_freq.gif|150px]] Symmetrical stretching of 2 B-H bonds in the plane of the molecule with another B-H stretch in the opposite direction (stretching motion)|| align="center" | 2715 (126)|| align="center" | [[File:JXS_GaBr3_6_freq.gif|150px]] Simultaneous scissoring motion and symmetrical stretching of 2 Ga-Br bond with another Ga-Br stretch in the plane of the molecule (stretching and bending motion)|| align="center" | 316 (57)
|}

A significant difference between the vibrational modes of the two molecules would be the frequency and intensity of the vibrational modes of the two molecules. As the frequencies correspond to the energies of the vibrational modes, the large difference of the frequencies for the two molecules indicate that the vibrational energies of the two molecules differ greatly. With the bonds being treated as simple harmonic oscillators, the formula for energy in wavenumbers is given by:
 <math>E(cm^{-1}) = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}</math>

Where E is energy in wavenumbers (cm-1), ''c'' is the speed of light, ''k'' is the spring constant and ''μ'' is the reduced mass. As the relative atomic mass of B and H are significantly smaller than that of Ga and Br, the reduced mass, ''μ'' is therefore smaller for BH3 and thus based on the formula, would lead to a higher energy value.

In addition, a reordering of vibrational modes was observed between the two molecules. The position of the first and third vibrational mode of BH3 have swapped around in GaBr3. Also, whilst the remaining vibrational modes retained their order, some of them have a slight modification to the type of vibrational mode they experience. The fifth vibrational modes of both molecules are similar due to the asymmetric stretching of the bonds. However, the one in GaBr3 is accompanied by a bending motion of the third Ga-Br bond which is not observed in BH3. Similarly the motions in the sixth vibrational mode of the two molecules are similar except that the symmetrical stretching of Ga-Br is accompanied by a scissoring motion of the bonds.

However, despite the differences, the resultant spectra were fairly similar. Both spectra had 3 observed peaks out of the possible 6 due to one of them being inactive on the IR spectra and the other two being degenerate vibrational modes. It also noticeable that the vibrational modes of both molecules are categorised into two distinct region; the higher energy region comprises of 2 vibrational mode with the E symmetry and an A1' symmetry whereas the lower energy region comprises of 2 vibrational mode with the E symmetry and A2" symmetry. The lower energy region corresponds to vibrational modes related to just the bending motion whereas the higher energy region corresponds to either stretching or a combination of stretching and bending motion. This shows that stretching is higher in energy compared to bending.

[[Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?]]

A frequency analysis is required in order to find out if the energy obtained in the optimisation step is a minimum. During the optimisation step, an energy value corresponding to the molecule was obtained. However, it does not indicate if that energy obtained was a minimum or maximum. A minimum would indicate that the molecule is in the ground state, whereas a maximum would indicate a high energy state such as a transition state. Therefore a frequency analysis is always carried out to find out if the energy obtained is a minimum, which is the state that is required in this assignment.

A molecule of N atoms would have 3N vibrational modes. However, 6 of the vibrational modes (for non-linear molecules) would correspond to a resultant translational or rotational motion in each of the 3 Cartesian axes. Hence they do not contribute to the vibrational mode and therefore the resultant number of vibrational mode for a molecule with N atoms is corrected to 3N-6. The low frequencies would thus correspond to the 3 rotational and 3 translational motion that arose from the vibrational modes.

===Molecular orbital of BH3===
In addition to a frequency analysis of the molecule, a population analysis can be carried out. With a population analysis, the molecular orbitals can be computed and visualised on GaussView. This would allow a qualitative comparison with the approximate MOs that were qualitatively drawn up via a MO diagram. This population analysis was carried out on BH3. With the optimised structure of the BH3 derived from the frequency analysis, the molecule was sent for population analysis via the HPC.

{| class="wikitable" border="1"
|+ '''Table XXX:''' [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27893 Results of BH3 population analysis]
|-
| File Type || .log
|-
| Calculation Type || SP
|-
| Basis Set || 6-31G(d,p)
|-
| Final Energy (au) || -26.61532363
|-
| Gradient || 0.00000000
|-
| Dipole Moment (Debye) || 0.0000
|-
| Point Group || D3h
|-
| Calculation time taken || 17.0 s
|}

The MO diagram was reproduced and the computed MOs were positioned next to the qualitatively-derived MOs from the MO diagram.

[[File:JXS_BH3_MO_diagram.jpg]]
 '''Figure XXX:''' MO diagram of BH3 with the computed MOs.

From the MO diagram above together with the computed MOs, it can be seen that the MOs derived qualitatively from MO diagrams are very similar to that of the computed MOs. While the MO diagram-derived MOs are superimposed fragment orbitals, the computed MOs showed the "resultant" of the superimposed fragments orbitals. Features such as through-space interaction between orbital lobes of the same phase were shown to have interaction on the computed MOs, while interaction between orbitals of opposite phase were shown to have a node between them.

[[This has therefore shown the usefulness of the qualitative MO theory as it is able to agree with computational results supported by calculations.]]

===Analysis of NH3===
Following the analysis carried out on BH3, a similar series of analysis can be conducted on other small molecules. NH3 was chosen as the molecule of interest. The sequence of optimisation, frequency and population analysis were carried out with a consistent basis set. In addition, a Natural Bonding Orbital (NBO) analysis was carried out on NH3.

====Optimisation and frequency analysis====
The optimisation of NH3 was carried out using the 6-31G(d,p) basis set before a frequency calculation was being down. The molecule was built on GaussView and calculations performed on Gaussian. The result summary of the reaction was tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3 optimisation and frequency calculation
! !! [[Media:JXS_NH3_OPTIMISATION.LOG|Optimisation]] !! [[Media:JXS_NH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -56.55776872 || -56.55776872
|-
| Gradient || 0.00000095 || 0.00000095
|-
| Dipole Moment (Debye) || 1.8465 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 15.0 s || 9.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000005 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-9.687922D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000005 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.088014D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -6.5478 -4.7624 -0.0006 0.0009 0.0018 1.3376
Low frequencies --- 1089.3505 1693.9257 1693.9298
</pre>
|}

====Population analysis====
Finally, similar to BH3, a population analysis was carried out. The optimised structure calculated from the frequency analysis was used to generate the calculated results. Results of the calculation can be obtained [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27894 here]

====Charge distribution of NH3====
From the population analysis, a NBO analysis can be carried out as well. This is done by looking at the charge distribution within the molecule itself. The charge distribution of the molecule is characterised by the colours on each individual atoms as well as the relative charge numbers shown on the atom (Fig. XXX).

[[File:JXS NH3 charge.jpg|400px]]
 '''Figure XXX:''' Charge distribution of NH3

The charge distribution is represented by a colour spectrum ranging from red to green, where red indicates a region of high charge density and green indicating a region of low density. Here it can be seen that N is red in colour, whereas the H atoms are green in colour. Corresponding to theory, N is highly electronegative as compared to H and therefore would have a high electron density. Therefore the NBO analysis showed that it is in agreement with theory. The numbers on the atoms show the charge range. In this diagram, the charge ranges from a value of -1.125 to 1.125, where -1.125 indicate a region of high electron density and the opposite end correspond to a region of low electron density.

===Calculation of NH3BH3===
In the final study, an analysis the adduct NH3BH3 was made. By carrying out the same series of analysis, the association energy between NH3 and BH3 can be derived. The steps for which they are derived will be elaborated further below.

====Optimisation and frequency analysis====
The adduct was first built on GaussView and then optimised via the 6-31G(d,p) basis set on Gaussian. After which a frequency analysis was carried out using the same basis set. The final results of the two calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of NH3BH3 optimisation and frequency calculation
! !! [[Media:NH3BH3_OPTIMISATION.LOG| Optimisation]] !! [[Media:NH3BH3_FREQ.LOG|Frequency Calculation]]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -83.22468911 || -83.22468911
|-
| Gradient || 0.00000125 || 0.00000134
|-
| Dipole Moment (Debye) || 5.5647 || 1.8465
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 1 min 2.0 s || 32.0 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000023 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.987776D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.151107D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -3.2121 -2.7006 -0.0011 -0.0005 0.0008 3.6891
Low frequencies --- 263.3411 632.9623 638.4431</pre>
|}

====Association energy of NH3BH3====
From the previous calculations, the energies were obtained to derive the association energy as shown below.

<center>
{| class="wikitable" border="1"
|-
| align="center" | E(NH3) = -56.55776872
E(BH3) = -26.61532363
 E(NH3BH3) = -83.22468911
 ΔE = -0.05159671
|}
</center>

The difference in energy ΔE is given by E(NH3BH3) - [E(BH3)+E(NH3)]. However, the value given above is in Hartree. Upon conversion to kJ/mol, the energy difference is '''135.47 kJ/mol.''' This would correspond to a typical weak single bond[[(cite atkins 932)]] which may indicate that such bond association (dative bond) is actually a weaker type of bond as both electrons come from one atom. One possible explanation for the weaker bond would be the fact that N is a highly electronegative atom, and thus the electrons would still prefer to be closer to N and hence giving rise to a lower bond strength.

[[must always remember to talk abt relative energies and not absolute energies]]

==References==

Rep:Mod:js3311inorgcompminiproj

2014-03-06T22:18:05Z

Js3311: /* MO and NBO calculation */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables XXX, XXX and XXX show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]
</center>

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

what chemical impact could these changes have?

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-06T22:17:31Z

Js3311: /* MO and NBO calculations */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables XXX, XXX and XXX show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

what chemical impact could these changes have?

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.

Rep:Mod:js3311inorgcompminiproj

2014-03-06T22:17:11Z

Js3311: /* MO and NBO calculations */

==Year 3 Inorganic Computational Mini Project - Ionic Liquids: Designer Solvents ==

==Comparison of selected 'onium' cations==
A computational study on ionic liquids was made as part of the mini project chosen for this computational assignment. Ionic liquids are, in general, ions that exist in liquid in room temperature. It is usually made up of an organic cation and an inorganic anion. Due to the vast possibilities of pairing up various types of cations and anions to give unique properties, it is not possible to experimentally determine all the properties of each ions. Hence there is an increased usage of computational methods to aid in the understanding of these ions. In this mini project, the properties of N(CH3)4+, P(CH3)4+ and S(CH3)3+ were investigated using similar computational methods that were used in the first part of this assignment.

===Optimisation and frequency analysis===
The first step involved the optimisation of the molecule followed by a frequency analysis. The three molecules of interest were first built on GaussView and sent to the HPC for optimisation. Subsequently on the optimised structure, a frequency analysis was carried out via the HPC again. Both calculations were carried out using the 6-31G(d,p) basis set. Tables XXX, XXX and XXX show the results of the optimising step together with the frequency analysis.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of N(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27874 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27895 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -214.18127322 || -214.18127322
|-
| Gradient || 0.00000003 || 0.00000032
|-
| Dipole Moment (Debye) || 3.4186 || 3.4186
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 12 min 24.0 s || 21 min 28.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-5.840350D-13
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-4.384135D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -5.4430 -2.0385 -0.0007 -0.0006 -0.0003 3.9825
Low frequencies --- 183.7666 288.3988 288.9025
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of P(CH3)4+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27875 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27878 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -500.82701172 || -500.82701172
|-
| Gradient || 0.00000110 || 0.00000115
|-
| Dipole Moment (Debye) || 3.1972 || 3.1972
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 24 min 11.2 s || 20 min 25.8 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000058 0.000060 YES
RMS Displacement 0.000015 0.000040 YES
Predicted change in Energy=-6.798695D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000281 0.001800 YES
RMS Displacement 0.000108 0.001200 YES
Predicted change in Energy=-3.688579D-10
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -2.5025 -0.0019 0.0030 0.0031 5.1097 7.5701
Low frequencies --- 156.4491 192.0483 192.2793
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of S(CH3)3+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27876 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27879 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -517.68327359 || -517.68327359
|-
| Gradient || 0.00000073 || 0.00000072
|-
| Dipole Moment (Debye) || 3.4663 || 3.4663
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 13 min 2.4 s || 10 min 14.1 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000054 0.000060 YES
RMS Displacement 0.000022 0.000040 YES
Predicted change in Energy=-1.824758D-10
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000601 0.001800 YES
RMS Displacement 0.000259 0.001200 YES
Predicted change in Energy=-2.340552D-09
Optimization completed.
</pre>
|-
| || <pre> Low frequencies --- -9.4907 -3.5011 0.0034 0.0046 0.0049 3.5578
Low frequencies --- 162.1235 199.5869 199.7515
</pre>
|}

====Discussion====

The various properties of the molecule including the C-X bond length, C-X-C bond angle and the shape with respect to the central atom were tabulated and presented in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Various physical properties of the cations
! !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>NCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> N(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>PCH34_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> P(CH3)4+ !!<jmol>
<jmolApplet>
<title>Orbital</title><color>black</color><size>200</size>
<uploadedFileContents>SCH33_optimisation_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol> S(CH3)3+ !!
|-
| Shape with respect to central atom || Tetrahedral || Tetrahedral || Trigonal pyramidal
|-
| C-X-C bond angle (°) || 109.5 (X = N) || 109.5 (X = P) || 102.7 (X = S)
|-
| C-X bond length (Å) || 1.51 || 1.82 || 1.82
|}

Based on the optimised structure, it can be seen that both N(CH3)4+ and P(CH3)4+ adopt a tetrahedral shape around the central atom. This is in accordance to the VSEPR theory where 4 bond pairs will adopt the tetrahedral shape in order to minimise repulsion between the bonds. As such the angle between all bonds is the widest possible. S(CH3)3+ adopts a trigonal pyramidal shape about the central S atom. However its basic geometry is also a tetrahedral shape. The only difference with the first two cations would be the absence of the 4th bond pair. In S(CH3)3+, it is replaced by the lone pair on the S atom hence it takes up the same basic geometry.

Despite the similar geometries that all three compounds take up, their bond angle about the central atom differs slightly. While N(CH3)4+ and P(CH3)4+ have similar bond angle of 109.5 °, S(CH3)3+ have a smaller bond angle about the central atom at 102.7 °. This can be attributed to the shape of the molecule. The 4 angles about the tetrahedral-shaped molecule will adopt the 109.5 ° bond angle. While S(CH3)3+ have a similar basic geometry and should adopt the same bond angle, the presence of the lone pair on sulphur caused the C-S-C bond angle to decrease. This is because the lone pair-bond pair repulsion is stronger than the repulsion between two bond pairs as the lone pair electrons are much more localised on the sulphur atom. The deviation from the ideal bond length of 109.5 ° increases with the electronegativity of the central atom. Hence for a hypothetical O(CH3)3+ cation, the bond angle about the central atom is expected to be smaller than 102.7 °.

The bond length can also be compared between the three cations. From the calculations it can be seen that the C-N bond length is the shortest (1.51 Å) whereas the C-P and C-S bond lengths are similar (1.82 Å). This is because N is on the second period on the period table whereas P and S are on the third period. As a result the valence electrons of N is closer to the nucleus and hence resulting in a shorter bond with C. Valence electrons of P and S are on the 3rd quantum shell and hence have more diffuse orbitals leading to a longer bond length.

===MO and NBO calculations===
Following the frequency analysis, the next step involve a population analysis in order to visualise the MO and also to carry out a NBO calculations. The optimised structures of the three cations were subjected to a population analysis calculation via the HPC using the same basis set. The results of the calculation were published onto D-Space and links given below.

<center>
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27880 Population analysis for N(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27890 Population analysis for P(CH3)4+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27882 Population analysis for S(CH3)3+]
</center>

====MO Discussion====
5 of the non-core occupied MOs have been visualised at an isovalue of 0.02 and tabulated below. A brief description of the nature of the MO is also elaborated.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Selected MO of N(CH3)4+
! MO !! Visualisation of MO !! Description of MO !! MO !! Visualisation of MO !! Description of MO
|-
| 6 || [[File:JXS_MO6.jpg|200px]] || Highly bonding molecular orbital with no nodal plane observed. This could be due to the linear combination of s atomic orbitals within the cation. Strong through-space interaction lead to one large electron density at this energy level. || 15 || [[File:JXS_MO15.jpg|200px]] || Molecular orbital consisting of 4 lobes of alternating phase and separated by two nodal planes. The molecule orbital is not found on the central molecule nor on 4 of the H atoms as illustrated.
|-
| 10 || [[File:JXS_MO10.jpg|200px]] || Molecular orbital with circular lobe around the central atom with lobes of opposite phase at the methyl groups. This give rise to a radial node that separates the two phases. Weak through-space interaction between lobes on methyl groups which can be visualised by setting isovalue to 0.01. Populating this molecular orbital with electrons will weaken the N-C bond but strengthen C-H bond as radial node occurs along the N-C bond. || 18 || [[File:JXS_MO18.jpg|200px]] || Molecular orbital found only on 3 out of 4 methyl groups. On each methyl group, two lobes of opposite phase present, leading to 3 lobes of both phases. The lobes are arranged on a plane of the 3 methyl groups in an alternate matter. This results in 3 intersecting nodal plane and hence, no through-space interaction.
|-
| 14 || [[File:JXS_MO14.jpg|200px]] || Molecular orbital found on all 4 methyl groups, with 2 lobes of opposite phases on each methyl group, resulting in 4 nodal planes alone the methyl group. Green lobes on each methyl groups have strong through-space interaction, whereas red lobes have good through-space interaction, giving rise to a sandwich structure with 3 large alternating lobes. No contribution from the central atom to this molecular orbital.
|}

====NBO Discussion====
The charge distribution of the molecules that resulted from the population analysis of the molecules were collated and tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of the three cations (charge range -1.8 to 1.8)
! !! N(CH3)4+ !! P(CH3)4+ !! S(CH3)3+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour.jpg|200px]] || [[File:PCH34_charge_dist_by_colour.jpg|200px]] || [[File:SCH33_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values.jpg|200px]] || [[File:PCH34_charge_dist_by_value.jpg|200px]] || [[File:SCH33_charge_dist_by_value.jpg|200px]]
|}

Even though the central atom was the only thing that changed between the three cations, the charge distribution differed greatly. It can be seen that N(CH3)4+ have a smaller range as characterised by the dark green and red colour on the atoms, whereas the other two cations have more polarised charge distribution given by the bright green and red colours on the atoms. It is also interesting to note that when the central atom is N, the charge on the central atom is mildly negative as given by the dark red colour. However in contrast, when the central atom is P or S, the central atom becomes mildly positive (S) to strongly positive (P). This is due to the electronegativity of the central atom. As N is highly electronegative, it has a tendency to pull electron density towards it and hence the central atom (N) remains negative. However as P and S are less electronegative, the central atom becomes electron-deficient as characterised by the green colour on the central atom. However, as P is slightly less electronegative than S, it has lower electron density, shown by a higher positive value for charge distribution of 1.667 compared to that of S at 0.917.

When the charge is being placed over the N atom, it would indicate that N is electron-deficient and holds a positive charge as it has lost its neutral charge in the bonding with another CH3 group. When looking at the NBO calculations, it does not agree with the traditional way of placing a formal charge over the N atom. From table XXX it shows that the N atom is mildly negatively-charged given by the dark red colour on the atom. In contrast to the traditional way of placing a formal charge, the positive charge is smeared over the whole molecule, specifically on the H atoms of the molecule. Hence with no accurate way of drawing the distribution of positive charge over all the H atoms, it would be best represented with a formal positive charge on N as the presence of N gives rise to functionality in the molecule, which is key in illustrating mechanistic pathways in arrow-pushing.

==Influence of functional groups==
Presence of functional groups can also alter the properties of the cation of interest. In the previous section, the properties of neutral cations were being investigated. Herein, two different functional groups were investigated, the electron-donating hydroxyl group (OH) and the electron-donating nitrile group (CN) were added to N(CH3)4+ and the same calculations were ran to determine how these functional groups affect the properties of the solid.

===Optimisation and frequency analysis===
Both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ were optimised using the same 6-31G(d,p) basis set and calculations performed via the HPC. The results of the calculations were tabulated below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2OH)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27888 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27887 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -289.39470714 || -289.39470714
|-
| Gradient || 0.00000023 || 0.00000029
|-
| Dipole Moment (Debye) || 5.2654 || 5.2654
|-
| Point Group || C1 || C1

|-
| Calculation time taken || 44 min 14.7 s || 27 min 14.3 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000006 0.000040 YES
Predicted change in Energy=-9.876055D-12
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-7.443290D-12
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -7.8462 -6.5078 -0.0009 -0.0005 0.0008 3.3666
Low frequencies --- 130.7361 214.3748 255.8446
</pre>
|}

{| class="wikitable" border="1"
|+ '''Table XXX:''' Results of [N(CH3)3(CH2CN)]+ optimisation and frequency calculation
! !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27883 Optimisation] !! [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27884 Frequency Calculation]
|-
| File Type || .log || .log
|-
| Calculation Type || FOPT || Freq
|-
| Basis Set || 6-31G(d,p) || 6-31G(d,p)
|-
| Final Energy (au) || -306.39376198 || -306.39376198
|-
| Gradient || 0.00000016 || 0.00000028
|-
| Dipole Moment (Debye) || 18.3589 || 18.3589
|-
| Point Group || C1 || C1
|-
| Calculation time taken || 28 min 13.8 s || 30 min 35.9 s
|-
| rowspan="2" align="center" | .log files || <pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-1.211787D-11
Optimization completed.
</pre> || <pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000010 0.001200 YES
Predicted change in Energy=-1.034558D-11
Optimization completed.
</pre>
|-
| || <pre>
Low frequencies --- -4.8948 -1.8293 -0.0009 -0.0008 -0.0008 5.0542
Low frequencies --- 91.6378 153.9753 211.4833
</pre>
|}

===MO and NBO calculation===
Following the optimisation and frequency analysis made to confirmed that the lowest energy optimised structure were achieved, a population analysis was carried out on both molecules as well. Calculations were made via the HPC and the result of the calculation were published onto D-Space and given below.

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27886 Population Analysis for N(CH3)3(CH2OH)+]

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/27885 Population Analysis for N(CH3)3(CH2CN)+]

===Effect of functional groups on charge distribution===
The effect of functional groups on the charge distribution can also be investigated. Similar to previous section, population analysis were ran and the NBO analysis was done on the two molecules and charge distribution by colours and also values were summarised in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' NBO analysis of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ (charge range -0.8 to 0.8)
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Charge distribution by colour || [[File:NCH34_charge_dist_by_colour_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_colour.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_colour.jpg|200px]]
|-
| Charge distribution by values || [[File:NCH34_charge_dist_by_values_8.jpg|200px]] || [[File:NCH34_OH_charge_dist_by_value.jpg|200px]] || [[File:NCH34_CN_charge_dist_by_value.jpg|200px]]
|}

From here it can be seen that by adding an OH or CN group, the charge distribution differed a little. For [N(CH3)3(CH2OH)]+, it can be seen that the carbon atom directly bonded to the OH group is slightly positively charged (0.088) whereas the other carbon atoms are slightly negatively charged (-0.494 to -0.491). In contrast for [N(CH3)3(CH2CN)]+, all carbon atoms are slightly negatively charged (-0.489 to -0.358). However, the carbon directly bonded to CN group is slightly less negatively charged (-0.358). Both N central atom however, remained slightly negatively charged (-0.322 for [N(CH3)3(CH2OH)]+ and -0.289 for [N(CH3)3(CH2CN)]+).

Following the NBO analysis, it is interesting to note that the NBO analysis does not match with theoretical understanding of electron-donating and electron-withdrawing groups. As the OH group is a known electron-donating group, it is expected that it would donate its electron density towards neighbouring atoms. However as shown from the NBO analysis, the O atom is negatively charged (-0.725) whereas its adjacent atoms are all positively charged (0.088 for C and 0.521 for H) for [N(CH3)3(CH2OH)]+. Similarly when looking at [N(CH3)3(CH2CN)]+, CN group is an electron-withdrawing group. Despite the presence of N on CN pulling electron density away from the adjacent C molecule as illustrated by the difference in the charge distribution, it can be seen that the extent of electron-withdrawing capabilities does not extend out any further. The carbon bearing the CN group is negatively charged (-0.358) as previously mentioned. In theory, that particular carbon should be slightly electron-deficient due to the presence of the electron-withdrawing CN group. One observation that is consistent with theory though, would be the charge distribution on the central atom. While the charge on the central atom N is -0.295 for N(CH3)4+, that of [N(CH3)3(CH2OH)]+ is indeed lower at -0.322 while that of [N(CH3)3(CH2CN)]+ is higher at -0.289.

===Effect of functional groups on HOMO and LUMO===
In addition to the NBO analysis, an analysis of the HOMO and LUMO was done by understanding how they vary in terms of structure and energy levels when different functional groups are placed on the cation. The HOMO and LUMO of N(CH3)4+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ together with the corresponding energy values were tabulated in the table below.

{| class="wikitable" border="1"
|+ '''Table XXX:''' Comparison of HOMO and LUMO
! !! N(CH3)4+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| Visualised LUMO || [[File:NCH34_LUMO.jpg|200px]] || [[File:NCH34_OH_LUMO.jpg|200px]] ||
[[File:NCH34_CN_LUMO.jpg|200px]]
|-
| LUMO Energy Value (au) || align="center" | -0.13302 || align="center" | -0.12459 || align="center" | -0.18182
|-
| Visualised HOMO || [[File:NCH34_HOMO.jpg|200px]] || [[File:NCH34_OH_HOMO.jpg|200px]] ||
[[File:NCH34_CN_HOMO.jpg|200px]]
|-
| HOMO Energy Value (au) || align="center" | -0.57934 || align="center" | -0.48763 || align="center" | -0.50047
|-
| abs(ΔE) (au) || align="center" | 0.44632 || align="center" | 0.36304 || align="center" | 0.31865
|}

It can be seen that one significant observation between the HOMO and LUMO of all three cations would be that the HOMO are slightly localised on specific regions. However the LUMO are very diffuse and delocalised. As shown in the table, the LUMO extend out a very large area all over the cations.

It is also interesting to note the changes in the shape of the molecular orbitals when different functional groups were placed on the cation. These changes are reflected mainly on the HOMO of each cation. The HOMO of N(CH3)4+ can be described to be localised on the methyl groups. However when looking at [N(CH3)3(CH2OH)]+, the HOMO is largely localised on the OH group and the atoms adjacent to it. This is in contrast to N(CH3)4+ where the orbitals are spread out amongst the methyl groups. For [N(CH3)3(CH2CN)]+, the HOMO is even more localised on the CN group and the carbon adjacent to it such that there is almost negligible molecular orbitals found elsewhere. The LUMOs in contrast, have very small observable changes. This is because the molecular orbitals are all delocalised around the whole molecule. It can be observed though, that there is two nodal plane at the CN group of [N(CH3)3(CH2CN)]+, whereas the LUMO of [N(CH3)3(CH2OH)]+ do not have these nodal places at the OH group.

Also, some observations can be made regarding the effect of adding functional groups on energy levels of the HOMO and LUMO of the cations. From the table it can be seen that adding both function groups led to a rise in the energy level of the HOMO. However the raise in energy level of the HOMO for [N(CH3)3(CH2OH)]+ (from -0.57934 to -0.48763 au) was greater than that of [N(CH3)3(CH2CN)]+ (from -0.57934 to -0.50047 au). The presence of the functional groups also have an effect on the LUMO of the cations. While the presence of an OH group led to an increase in the energy level of the LUMO for [N(CH3)3(CH2OH)]+ (from -0.13302 to -0.12459 au), the presence of the CN group led to a decrease in the energy level of the LUMO for [N(CH3)3(CH2CN)]+ instead (from -0.13302 to -0.18182 au). The changes to the energy levels of both the HOMO and LUMO led to a change in the HOMO-LUMO gap of the cations. While the HOMO-LUMO gap has decreased in general when adding either a CN or OH group, the HOMO-LUMO gap for [N(CH3)3(CH2CN)]+ is the smallest amongst the three cations at 0.31865 au.

what chemical impact could these changes have?

==Conclusion==
In conclusion, with the understanding of basic calculations in computational chemistry, the knowledge was applied in the study of different types molecules. These basic calculation functions include an optimisation, frequency and population analysis, for which more information about the cations can be extracted. These various calculations were used to study the molecular orbitals and also the natural bonding orbitals of various ionic liquid cations in this mini project. In addition, by varying the functional groups on one of the cation, the changes observed in the MO and NBO calculations were discussed.