ChemWiki - User contributions [en]

Rep:Mod:qwt11 inorg

2013-11-22T11:07:37Z

Qwt11:

Qian Wen Tan 
CID: 00700342 
==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.{{DOI|10.1063/1.446117}}</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. The energies were checked to ensure that further calculations made were based on the optimised structure found using the 6-31G(d,p) basis set.

==References==
<references />

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T11:07:02Z

Qwt11: /* References */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+, less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

 
==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. Energy differences were ignored as the optimised molecules obtained from using the basis set 6-31G(d, p) were used for frequency analysis and population analysis. Overall, the calculations helped to explore the geometries of the 'onium' ions by looking at the key bond lengths and angles; observe the charge distribution in the ions and compare the influences of placing electron withdrawing and electron donating groups on the ions.
 

 
==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T11:06:47Z

Qwt11: /* Conclusion */

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T11:06:33Z

Qwt11: /* Conclusion */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+, less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. Energy differences were ignored as the optimised molecules obtained from using the basis set 6-31G(d, p) were used for frequency analysis and population analysis. Overall, the calculations helped to explore the geometries of the 'onium' ions by looking at the key bond lengths and angles; observe the charge distribution in the ions and compare the influences of placing electron withdrawing and electron donating groups on the ions.
 

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T11:06:02Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+, less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. Energy differences were ignored as the optimised molecules obtained from using the basis set 6-31G(d, p) were used for frequency analysis and population analysis. Overall, the calculations helped to explore the geometries of the 'onium' ions by looking at the key bond lengths and angles; observe the charge distribution in the ions and compare the influences of placing electron withdrawing and electron donating groups on the ions.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T11:05:30Z

Qwt11: /* Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+, less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. Energy differences were ignored as the optimised molecules obtained from using the basis set 6-31G(d, p) were used for frequency analysis and population analysis. Overall, the calculations helped to explore the geometries of the 'onium' ions by looking at the key bond lengths and angles; observe the charge distribution in the ions and compare the influences of placing electron withdrawing and electron donating groups on the ions.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T11:04:26Z

Qwt11: /* Conclusion */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+, less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. Energy differences were ignored as the optimised molecules obtained from using the basis set 6-31G(d, p) were used for frequency analysis and population analysis. Overall, the calculations helped to explore the geometries of the 'onium' ions by looking at the key bond lengths and angles; observe the charge distribution in the ions and compare the influences of placing electron withdrawing and electron donating groups on the ions.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T10:57:42Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+, less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T10:55:56Z

Qwt11: /* NBO Charge Analysis */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument; the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T10:54:46Z

Qwt11: /* Comparison of geometries */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 valence electrons left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T10:54:03Z

Qwt11: /* Comparison of geometries */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on them. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg

2013-11-22T10:51:03Z

Qwt11:

Qian Wen Tan 
CID: 00700342 
==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.{{DOI|10.1063/1.446117}}</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. The energies were checked to ensure that further calculations made were based on the optimised structure found using the 6-31G(d,p) basis set.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:50:51Z

Qwt11:

Qian Wen Tan 
CID: 00700342
==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.{{DOI|10.1063/1.446117}}</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. The energies were checked to ensure that further calculations made were based on the optimised structure found using the 6-31G(d,p) basis set.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:50:36Z

Qwt11:

Qian Wen Tan
CID: 00700342
==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.{{DOI|10.1063/1.446117}}</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. The energies were checked to ensure that further calculations made were based on the optimised structure found using the 6-31G(d,p) basis set.

==References==
<references />

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T10:48:30Z

Qwt11: /* Comparison of geometries */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.813Å<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref> in (SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-22T10:44:37Z

Qwt11: /* Comparison of geometries */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.{{DOI|10.1021/ja0402607}}</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.{{DOI|10.1107/S0108270195010304 }}</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.{{DOI|10.1039/B505287B }}</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg

2013-11-22T10:39:51Z

Qwt11: /* Association energies: Ammonia-Borane */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.{{DOI|10.1063/1.446117}}</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. The energies were checked to ensure that further calculations made were based on the optimised structure found using the 6-31G(d,p) basis set.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:37:47Z

Qwt11: /* Conclusion */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy. The energies were checked to ensure that further calculations made were based on the optimised structure found using the 6-31G(d,p) basis set.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:36:18Z

Qwt11: /* Association energies: Ammonia-Borane */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values. The calculations can be repeated to check for accuracy.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:35:17Z

Qwt11: /* Association energies: Ammonia-Borane */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. The difference in energies obtained for the 6-31G(d,p) calculation and frequency analysis is negligible. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:33:53Z

Qwt11: /* Association energies: Ammonia-Borane */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/images/6/62/NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:30:43Z

Qwt11: /* Frequency analysis for GaBr3 */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the molecule is in bending modes as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:28:27Z

Qwt11: /* Analysis of results */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, a bond will still be formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the top Br atom performs alternating in-plane scissoring with the bottom 2 Br atoms while the Ga atom moves slightly left and right as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references />

Rep:Mod:qwt11 inorg

2013-11-22T10:25:04Z

Qwt11: /* Using basis set 3-21G */

==Optimisation of BH3 molecule==
Optimisation was performed on 2 different BH3 molecules. The B-H bond lengths for the first(A) were not modified while the bond lengths for the second(B) were modified to 1.53Å, 1.54Å and 1.55Å.
===Using basis set 3-21G===

Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/images/3/32/BH3_OPT_321G.LOG | 3-21G .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/images/5/58/QWT_BH3_OPT.LOG | 3-21G .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |3-21G
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.46226433 a.u.
| style="text-align: center;" |-26.46226429 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00004507 a.u.
| style="text-align: center;" |0.00008851 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
|}
 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000352 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
Predicted change in Energy=-4.580958D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<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=-1.672478D-07
Optimization completed.
-- Stationary point found.
</pre>
Optimisation was performed on 2 different starting BH3 molecules using the basis set 3-21G. as they give different results. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. Since the most basic basis set was used, the point group of (B) is CS instead of the expected D3h. This indicates that the level of calculation is insufficient for the programme to come up with the correct point group. The energy is calculated to be -26.46226433 a.u. for (A) and -26.46226429 a.u. for (B). The difference in energy is negligible.
 

===Using basis set 6-31G(d,p)===
Log file 
A:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:BH3_OPT_631G.LOG | 6-31G(d,p) .log file for (A)]] 
B:[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QWT_BH3_OPT_631G_DP.LOG | 6-31G(d,p) .log file for (B)]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000475 a.u.
| style="text-align: center;" |0.00008206 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 6.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
|}

 
Final sets of forces and displacements for (A)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000025 0.001200 YES
Predicted change in Energy=-5.342731D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-H: 1.19Å 
 
Optimised angle 
H-B-H: 120.0o 
Optimisation of BH3 was performed using the basis set 6-31G(d,p), which is more accurate than 3-21G. The RMS gradient norm is <0.001 and close to 0 for both. In addition, both calculations also converged. The energy is calculated to be -26.61532363 a.u. for (A) and -26.61532358 a.u. for (B). Once again, the slight difference in energy is negligible. The optimised length of 1.19Å is identical to the one reported in literature<ref name= "CRC Handbook">D. R. Lide, CRC Handbook of Chemistry and Physics, 89th Edition (Internet Version 2009), CRC Press/Taylor and Francis, Florida, 89th edn., 2009.</ref>, indicating accuracy in the calculation. One important observation is that the point group of (B) remained as CS despite using the basis set 6-31G(d,p). This implies that the programme was unable to detect the correct point group of the molecule as this is considered to be a low level calculation. This will later affect the frequency analysis of BH3 as shown below. 

==Optimisation of GaBr3 molecule==
DOI 
{{DOI|10042/26068}} 

Summary of results 

GaBr3 optimisation
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.69989295 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00402846 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 23.1 seconds
|}
 
Final sets of forces and displacements
<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=-1.282688D-12
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
Ga-Br: 2.39Å 
 
Optimised angle 
Br-Ga-Br: 120.0o 

Optimisation of GaBr3 was performed using the basis set LANL2DZ as Ga and Br are heavy atoms that require the use of pseudo-potentials for more accurate calculations. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -41.69989295 a.u.. The reported Ga-Br bond length for GaBr3 is 2.249Å<ref name= "CRC Handbook"/>. This is slightly shorter than the computed length but the difference is not significant. Overall, the computed length of 2.39Å is reasonable. 

==Optimisation of BBr3 molecule==
The BBr3 molecule was created by modifying BH3 (A). 
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/8/85/BBr3_opt_gen.log |Gen .log file]] 
Summary of results 
BBr3 optimisation 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |Gen
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-64.43645296 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000382 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 40.5 seconds
|}
 
Final sets of forces and displacements
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027258D-10
Optimization completed.
-- Stationary point found.
</pre>

Optimised length 
B-Br: 1.93Å 
 
Optimised angle 
Br-B-Br: 120.0o 

Optimisation of BBr3 was performed using the basis set Gen as B is a light atom while Br is a heavy atom. This allows the specification of basis sets for the individual atoms. The RMS gradient norm is <0.001 and close to 0 and the calculation converged. The energy is calculated to be -64.43645296 a.u.. Comparing the optimised B-Br length to the reported length of 1.893Å<ref name= "CRC Handbook"/>, it is slightly longer but still close enough.

==Analysis of results==
Comparison of bond lengths of BH3, BBr3, and GaBr3
 
<center>
{| class="wikitable"
! style="background: #fdb813; color: black;" |Molecules
! style="background: #fdb813; color: black;" |BH3
! style="background: #fdb813; color: black;" |BBr3
! style="background: #fdb813; color: black;" |GaBr3
|-
| Optimised Bond lengths (Å)
| style="text-align: center;" |1.19
| style="text-align: center;" |1.93
| style="text-align: center;" |2.39
|-
|}
Table 1: Bond lengths of BH3, BBr3, and GaBr3</center> 
The bond lengths increases from BH3 to BBr3 to GaBr3. It reflects the bond strength, for the longer the bond, the weaker it is. In turn, bond strength is affected by a few factors: (1) size of atoms, (2) difference in electronegativity between atoms, (3) extent of orbital overlap between atoms and (4) bond polarity.

By comparing BH3 and BBr3, it can be observed that changing from a small ligand (H) to a large ligand (Br) lead to an increase in the bond length. Both B-H and B-Br are covalent bonds. The increase in bond length is caused by a few factors. Firstly, the Br atom will naturally be displaced further from B than the H atom as it is bigger in size. This is due to greater electron-electron repulsion when the two atoms are side by side as Br atom has more electrons. Hence, the equilibrium length will be longer between B-Br than B-H. In addition, the bond length is also affected by the difference in electronegativity between B and H and B and Br. H and Br are both more electronegative than B but Br is significantly more electronegative than H. Hence, the B-Br bond is more polar than the B-H bond as the more electronegative Br will draw more electrons towards it than H. This is a result of greater polarisability of Br than H. As a result, there is a significant increase in bond length from 1.19Å to 1.93Å.

GaBr3 has a longer bond length than BBr3. In general, Ga is a bigger molecule with more electrons than B hence the bond length will increase as mentioned before.. In addition, although both Ga and B belong to group 13 of the Period Table of Elements, Ga is a metal while B is a non-metal. Hence, the Ga-Br bond is ionic while the B-Br bond is covalent. In general, ionic bonds are weaker than covalent bonds as there are electrostatic attraction between the ions while a covalent bond involves the 2 atoms sharing their electrons. In addition, the larger the atom, the more diffused its orbital. Hence, Ga-Br bond is the weakest as it has the least orbital overlap while the B-H bond is the strongest as it has the most orbital overlap.

A bond is an attractive interaction between atoms. According to the nature of interaction and the type of atoms involved, there are a few different types of bonds possible: covalent bond, ionic bond, metallic bond and agostic bond. All these forms of bond result in the formation of chemical molecules constructed from 2 or more atoms. In addition, there is also hydrogen bond, which is technically not a proper bond, but it is also formed due to attractive interactions between atoms. Overall, the formation of a bond will lead to a reduction in the overall energy of the system.

In some structures, Gaussview does not show the expected bonds. However this does not imply the absence of a bond. Rather, Gaussview has been structured to show the presence of a bond, if the distance between the 2 atoms is within a pre-defined value. Hence, as long as the bond distance between atoms is out of this value, Gaussview will not draw in the bond. However, this does not define the presence of the bond, as it is still dependent on the interaction between the atoms; if it is sufficiently strong, there will still be a bond formed. 

==Frequency analysis for BH3==
Log file 
[[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/BH3_FREQ.LOG | Frequency analysis .log file for (A)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/a1/QWT_BH3_FREQ%28B%29.LOG | Frequency analysis .log file for (B)]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/7/72/QWT_BH3_FREQ%28B%29_ULTRAFINE.LOG | Frequency analysis .log file for (B)(int=ultrafine scf(conver=9))]] 
Summary of results 
BH3 optimisation 
{| class="wikitable"
! BH3 molecules
| style="text-align: center;" |(A)
| style="text-align: center;" |(B)
| style="text-align: center;" |(B)(int=ultrafine scf(conver=9))
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
| style="text-align: center;" |-26.61532358 a.u.
| style="text-align: center;" |-26.61532349 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000477 a.u.
| style="text-align: center;" |0.00008202 a.u.
| style="text-align: center;" |0.00008330 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
| style="text-align: center;" |0.0003 Debye
| style="text-align: center;" |0.0003 Debye
|-
! Point Group
| style="text-align: center;" |D3h
| style="text-align: center;" |CS
| style="text-align: center;" |CS
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 5.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 15.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 7.0 seconds
|}

 
Final sets of forces and displacements for (A) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-5.368813D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000189 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000784 0.001800 YES
RMS Displacement 0.000317 0.001200 YES
Predicted change in Energy=-1.380433D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for (B)(int=ultrafine scf(conver=9)) 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000403 0.001200 YES
Predicted change in Energy=-1.411213D-07
Optimization completed.
-- Stationary point found.
</pre>

Frequencies for (A) 
<pre>
Low frequencies --- -3.5991 -1.1355 -0.0054 1.3745 9.7046 9.7707
Low frequencies --- 1162.9825 1213.1733 1213.1760
</pre>

Frequencies for (B) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0008 33.8606 41.5990 43.7038
Low frequencies --- 1163.5023 1213.4686 1213.5878
</pre>

Frequencies for (B)(int=ultrafine scf(conver=9)) 
<pre>
Low frequencies --- -0.0008 -0.0004 0.0009 28.8837 40.2093 44.9269
Low frequencies --- 1163.4954 1213.3988 1213.6046
</pre>

Frequency analysis was performed on (A) and (B). The RMS gradient norm is <0.001 and close to 0 for all and all the calculations converged. Although we were instructed to work with (B), which has it's bond lengths modified, frequency analysis indicated that the low frequencies fall out of the required range of +/- 15cm-1. This is observed even after using the keyword 'int=ultrafine scf(conver=9)' and checking the box for tight convergence criteria. As a result, the remaining analysis data were taken from (A) as advised by the demonstrator. It can be observed that the calculated energy, dipole moment and point group are identical to the one calculated before, indicating that the same molecule was used. 

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:Bh3_freq01.png|250px|01]] All the H atoms move in and out of the plane together while the B atom also moves in and out of plane but in opposite direction to the H atoms.
| style="text-align: center;" |1163
| style="text-align: center;" |92.5497
| style="text-align: center;" |A2"
|-
| 2
| style="text-align: center;" |[[File:Bh3_freq02.png|250px|01]] The 2 bottom H atoms are scissoring while the top H atom and the B atom moves up and down due to the motion.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0545
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:Bh3_freq03.png|250px|01]] The top H atom performs alternate in-plane scissoring with the bottom 2 H atoms while the B atom remains stationary. The 2 bottom H atoms are rocking in plane.
| style="text-align: center;" |1213
| style="text-align: center;" |14.0581
| style="text-align: center;" |E'
|-
| 4
| style="text-align: center;" |[[File:Bh3_freq04.png|250px|01]] All 3 H atoms move inward and outward in the plane (symmetric stretching), from the center while the B atom remains stationary.
| style="text-align: center;" |2582
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:Bh3_freq05.png|250px|01]] The 2 bottom H atoms perform asymmetric stretching while the top H atom remains stationary. The B atom moves slightly left and right in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3285
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:Bh3_freq06.png|250px|01]] The 2 bottom H atoms perform symmetric stretching while the top H atom performs asymmetric stretching. The B atom moves slightly up and down in plane.
| style="text-align: center;" |2716
| style="text-align: center;" |126.3189
| style="text-align: center;" |E'
|}
Table 2: Vibrational frequencies and modes of BH3</center> 
IR spectrum
<center>[[File:Bh3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 1: IR spectrum of BH3</center> 
For the BH3 molecule, there are a total of 3N-6 = 6, where N = 4, vibration modes observed as seen in the Table above. However, the IR spectrum only shows 3 peaks. This is due to two reasons. Firstly, vibration mode #4 is not observed as it does not result in a change in dipole moment. Hence the intensity as seen in Table 2 is 0.0000. Vibrational modes #2 and #3 have the frequency value of 1213cm-1. As a result, the individual peaks will overlap to give a single peak. This is similarly observed for vibrational modes #5 and #6, in which both have a frequency of 2716cm-1. Hence, only 3 peaks will be observed in the IR spectrum. 

==Frequency analysis for GaBr3==
DOI file 
{{DOI|10042/26117}} 
Summary of results 
GaBr3 frequency analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |LANL2DZ
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-41.70082783 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000011 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 16.3 seconds
|}
 
Final sets of forces and displacements 
<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.
-- Stationary point found.
</pre>

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

Table of vibrations 
<center>
{| class="wikitable"
! #
! Forms of vibration
! Frequency (cm-1)
! Intensity
! Symmetry (D3h point group)
|-
| 1
| style="text-align: center;" |[[File:GaBr3_freq01.png|250px|01]] 2 of the Br atoms and the Ga atom are moving left and right in plane while the last Br atom is moving in opposite direction (right then left). These are in-plane rocking and scissoring bending modes.
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 2
| style="text-align: center;" |[[File:GaBr3_freq02.png|250px|01]] The 2 bottom Br atoms are moving down and up(scissoring) while the top Br atom and Ga atom are moving up and down (opposite direction).
| style="text-align: center;" |76
| style="text-align: center;" |3.3447
| style="text-align: center;" |E'
|-
| 3
| style="text-align: center;" |[[File:GaBr3_freq03.png|250px|01]] All 3 Br atoms move in and out of the plane. The Ga atom does the same but in opposite direction.
| style="text-align: center;" |100
| style="text-align: center;" |9.2161
| style="text-align: center;" |A2"
|-
| 4
| style="text-align: center;" |[[File:GaBr3_freq04.png|250px|01]] The 3 Br atoms stretches symmetrically in plane while the Ga atom remains stationary.
| style="text-align: center;" |197
| style="text-align: center;" |0.0000
| style="text-align: center;" |A1'
|-
| 5
| style="text-align: center;" |[[File:GaBr3_freq05.png|250px|01]] The 2 bottom Br atoms perform asymmetric stretching while the Ga atom moves left and right in plane. The last Br atom remains stationary.
| style="text-align: center;" |316
| style="text-align: center;" |57.0704
| style="text-align: center;" |E'
|-
| 6
| style="text-align: center;" |[[File:GaBr3_freq06.png|250px|01]] All 3 Br atoms move up and down while the Ga atom moves in opposite direction (down then up).
| style="text-align: center;" |316
| style="text-align: center;" |57.0746
| style="text-align: center;" |E'
|}
Table 3: Vibrational frequencies and modes of GaBr3</center> 
IR spectrum
<center>[[File:GaBr3_freq_irspectrum.png|700px|IR spectrum]] 
Figure 2: IR spectrum of GaBr3</center> 
Frequency analysis was performed on GaBr3 using the pseudo-potential LANL2DZ. The RMS gradient norm is <0.001 and close to 0 for both. In addition, the calculation converged. Looking at the energy, dipole moment and point group, they are identical to the ones calculated above, indicating that the same molecule was used. The 6 low frequencies (first line) are also within the required range of +/-15cm-1, hence there is accuracy in the calculation. The lowest 'real' vibrational mode is 76cm-1 and it is when the top Br atom performs alternating in-plane scissoring with the bottom 2 Br atoms while the Ga atom moves slightly left and right as shown in the table above. 

==Frequency analysis comparison between BH3 and GaBr3==
Table of vibrational modes of BH3 and GaBr3
{| class="wikitable"
! Molecules
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
| style="text-align: center;" |Vibrations(cm-1) /Symmetry
|-
! BH3
| style="text-align: center;" |1163/ A2"
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |1213/ E'
| style="text-align: center;" |2582/ A1'
| style="text-align: center;" |2716/ E'
| style="text-align: center;" |2716/ E'
|-
! GaBr3
| style="text-align: center;" |76/ E'
| style="text-align: center;" |76/ E'
| style="text-align: center;" |100/ A2"
| style="text-align: center;" |197/ A1'
| style="text-align: center;" |316/ E'
| style="text-align: center;" |316/ E'
|-
|}
<center>Table 4: Vibrational modes of BH3 and GaBr3</center> 
The vibrational frequencies are inversely proportional to the reduced mass and proportional to the force constant of the bond. The large difference in the value of frequencies for BH3 compared to GaBr3 indicate two things: GaBr3 has a larger reduced mass than BH3 and the Ga-Br bond is weaker than B-H bond. This is expected as Ga and Br are much heavier atoms than B and H. In addition, the Ga-Br bond has been calculated and explained to be significantly longer than the B-H bond as mentioned above. Hence, the vibrational frequencies of GaBr3 are expected to be much smaller than those of BH3.

Both molecules have a total of 3N-6=6, where N=4, vibrational modes. However, there has been a reordering of the modes as the lowest real mode for BH3 is at 1163cm-1 with a A2" symmetry while the same symmetry for GaBr3 comes after 2 E' symmetry vibrational modes. For BH3, it involves the movement of 3 light H atoms in and out of the plane as the B atom moves in opposite direction while for GaBr3 it involves movement of the Ga atom in and out of the plane, in opposite direction to the movement of the Br atoms. Since the Ga and Br are heavier atoms, more energy will be required. Hence the frequency is shifted higher.

Both IR spectra are similar in that they only show 3 peaks despite each molecule having 6 vibrational modes. This is because both molecules have a single vibrational mode that does not result in a change in dipole moment, and hence will not be shown on the IR spectrum. In addition, there are 2 pairs of degenerate vibrational modes for each molecule, causing an overlap of the peaks and resulting in only 3 peaks shown in the spectra. It should also be noted that the peaks for BH3 are of a greater intensity than those of GaBr3. This is a result of greater change in dipole moment during the stretching and bending of BH3 than GaBr3.

In both spectra, it has been observed that two modes lie fairly closely together, the A2" and E' modes. This is also seen for the A1' and E' modes, but higher in energy. This is because the A1' and E' modes are classified as stretching modes while the A2" and E' are classified as bending modes. The A1' and E; modes require a change in bond length during the stretching, which will result in more energy required. This is because when the bond is stretched, there is deviation from the equilibrium length. When the atoms are too close there will be a repulsion force which needs more energy to overcome during stretching. However, for the A2" and E' modes, bending does not require a change in bond length. The repulsion when the atoms are close in proximity is also lower. Hence, less energy is required.

The same method and basis set for both the optimisation and frequency analysis calculations are used as as a change in the method and basis set will produce different results. The basis sets indicate the level of calculations used for the molecules, and there can be no basis of comparison if different method and basis sets were used for the 2 molecules. This is because their calculations will have different degree of accuracies. This is observed when comparing the energies obtained from optimising BH3 using 3-21G and 6-31G(d,p)basis sets. The one obtained using 6-31G(d,p) is more accurate.

A frequency analysis produces frequencies which are second derivatives of the potential energy surface. Hence, a positive frequency indicates a minimum while a negative frequency indicates a maximum. As a result, in order to ensure that the energies obtained are minimum, we require a frequency analysis and ensure that the values of the frequencies are all positive when calculated. This will indicate that the structure used for calculation is at its ground state. Similarly, it gives us an indication if the optimisation has failed. This will be observed when a negative frequency is obtained.

Each non-linear molecule has 3N-6 vibrational modes. The 'low frequencies' represent the 6 vibrational modes that are subtracted in the equation. They are small and not counted as part of the vibrational modes as they are simply motions caused by the the centre of mass of the molecule.
 

==Molecular Orbitals of BH3==
DOI file 
{{DOI|10042/26123}} 
Summary of results 
BH3 MO analysis 
{| class="wikitable"
! File Type
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-26.61532363 a.u.
|-
! Dipole Moment
| style="text-align: center;" |0.0000 Debye
|-
! Point Group
| style="text-align: center;" |D3h
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 1 minutes 33.8 seconds
|}
 
MO diagram of BH3
<center>[[File:Bh3_MOdiagram.png|700px|MO diagram of BH3]] 
Figure 3: MO diagram of BH3</center>
 

Referring to the MO diagram above, there are no significant differences between the real and LCAO MOs. The drawn LCAO MOs are similar to the real MOs produced as BH3 is a simple molecule with with a straightforward MO diagram. This indicates that qualitative MO theory are sufficiently accurate and useful to show the molecular orbitals of molecules and the distribution of their electron density. However, one has to put caution to such a statement as when the complexity of the molecule increases and mixing occurs between MOs, the qualitative MO theory may fail to provide an accurate view of the MOs.

==NBO Analysis of NH3==
Log files 
[[https://wiki.ch.ic.ac.uk/wiki/images/1/1e/NH3_OPT_631GDP02.LOG | 6-31G(d,p) .log file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/5/56/NH3_FREQ_631GDP02.LOG | Frequency analysis file for NH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/Nh3_pop_631gdp02.log | Population analysis file for NH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |Optimisation using 6-31G(d,p)
| style="text-align: center;" |Frequency Analysis
| style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
| style="text-align: center;" |-56.55776872 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000137 a.u.
| style="text-align: center;" |0.00000150 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
| style="text-align: center;" |1.8465 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 12.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 9.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 34.3 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.785252D-11
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3 
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000008 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-2.196442D-11
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -9.3870 -8.2244 -6.1051 -0.0017 -0.0015 -0.0006
Low frequencies --- 1089.3360 1693.9207 1693.9250
</pre>

Although the basis set 6-31G(d,p) was used, the point group calculated was C1 instead of the expected C3V. This implies that better basis set is still required to ensure greater accuracy in the calculation. In addition, the keyword 'int=9 scf(conver=9)' was used and tight convergence criteria was chosen in order to ensure that the calculations will converge. The RMS gradient norm is <0.001 and close to 0 for both. The energy is calculated to be -56.55776872 a.u. and the dipole moment is calculated to be 1.8465D for the optimisation and the frequency analysis, indicating that the same molecule was used. The low frequencies calculated are also within the required range of +/-15cm-1. The calculated bond length of 1.02Å is similar to the reported value of 1.012Å<ref name= "CRC Handbook"/>.
 
 
Charge Distribution 
<center>[[File:NH3_charge01.png|300px|Nh3 charge 01]] 
Figure 4: Charge distribution in NH3 by colour</center> 

<center>[[File:NH3_charge02.png|300px|Nh3 charge 01]] 
Figure 5: Labelled charge distribution in NH3</center> 

The charge range for NH3 is -1.125 to 1.125. Referring to Figure 4, it can be seen that the N atom is negatively charged while the H atoms are positively charged. This is expected as N is more electronegative than H. Figure 5 shows the actual charge values for each atom, -1.125 for N and 0.375 for H. By summing up the charges, we will get a value of 0, which is expected as NH3 is a neutral molecule. Hence, this indicates accuracy in the calculations.

==Association energies: Ammonia-Borane==
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:NH3BH3_OPT_321G.LOG | 3-21G file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/c/cf/NH3BH3_OPT_631GDP_ULTRAFINE.LOG | 6-31G(d,p) .log file for NH3BH3]] 
[[https://wiki.ch.ic.ac.uk/wiki/images/a/af/NH3BH3_FREQ_631GDP_ULTRAFINE.LOG | Frequency analysis file for NH3BH3]] 
Summary of results 
{| class="wikitable"
! Calculation
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |Frequency Analysis using 6-31G(d,p)
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |3-21G
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |0
| style="text-align: center;" |0
| style="text-align: center;" |0
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-82.76661835 a.u.
| style="text-align: center;" |-83.22468905 a.u.
| style="text-align: center;" |-83.22468909 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003005 a.u.
| style="text-align: center;" |0.00000289 a.u.
| style="text-align: center;" |0.00000475 a.u.
|-
! Dipole Moment
| style="text-align: center;" |5.8431 Debye
| style="text-align: center;" |5.5645 Debye
| style="text-align: center;" |5.5645 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 0 minutes 21.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 33.0 seconds
|}
 
Final sets of forces and displacements for optimisation of NH3BH3 using 3-21G
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000419 0.001800 YES
RMS Displacement 0.000179 0.001200 YES
Predicted change in Energy=-5.743898D-08
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for optimisation of NH3BH3 using 6-31G(d,p)
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000012 0.000040 YES
Predicted change in Energy=-3.124960D-10
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis of NH3BH3
 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.152412D-10
Optimization completed.
-- Stationary point found.
</pre>

Frequencies 
<pre>
Low frequencies --- -4.9288 -0.0014 -0.0011 -0.0008 2.1989 3.1957
Low frequencies --- 263.3470 632.9566 638.4182
</pre>
 
Optimisation was first performed using the basis set 3-21G before using the 6-31G(d,p) basis set on the optimised file as NH3BH3 is not a small molecule. The optimised calculation using the 6-31G(d,p) set was done using the keyword 'int=9 scf(conver=9)' and tight convergence criteria was chosen. This was required in order to obtain low frequencies values that are within the +/-15cm-1 range when frequency analysis was performed. 
 

Bond lengths and angles 

{| class="wikitable"
! Method/Basis set
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3">J. S. Binkley and L. R. Thornel, J. Chem. Phys., 1983, 79, 2932.</ref>)
|-
! B-N bond length/Å
| style="text-align: center;" |1.67
| style="text-align: center;" |1.69
|-
! B-H bond length/Å
| style="text-align: center;" |1.21
| style="text-align: center;" |1.21
|-
! N-H bond length/Å
| style="text-align: center;" |1.02
| style="text-align: center;" |1.00
|-
! N-B-H angle/o
| style="text-align: center;" |104.6
| style="text-align: center;" |104.3
|-
! B-N-H angle/o
| style="text-align: center;" |111.0
| style="text-align: center;" |110.9
|-
|}
By comparing the calculated values with the reported values, it can be seen that although the method is different but the basis set is the same, the bond lengths and angles are still close. Hence, the calculations can be predicted to be accurate. 
 

Association & Dissociation Energies 
E(NH3)= -56.55776872 a.u. 
E(BH3)= -26.61532363 a.u. 
E(NH3BH3)= -83.22468905 a.u. 
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468905 a.u. -(-56.55776872 a.u.-26.61532363 a.u.) = -0.0515967 a.u. = -135.4671462kJ/mol 
Hence, the dissociation energy is 135kJ/mol. 

Comparision of energies 
{| class="wikitable"
! Compounds
| style="text-align: center;" |DFT RB3LYP/6-31G(d,p) (Computed)/a.u.
| style="text-align: center;" |HF/ 6-31G (Literature<ref name= "NH3BH3"/>)/a.u.
|-
! BH3
| style="text-align: center;" |-26.61532363
| style="text-align: center;" |-26.39001
|-
! NH3
| style="text-align: center;" |-56.55776872
| style="text-align: center;" |-56.18436
|-
! NH3BH3
| style="text-align: center;" |-83.22468905
| style="text-align: center;" |-82.61182
|-
|}
Using literature values,
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -82.61182 a.u. -(-56.18436 a.u.-26.39001 a.u.) = -0.03745 a.u. = -98.3249825kJ/mol 
Hence the literature dissociation energy is 98.3kJ/mol.

It can be observed that there is a deviation of the bond dissociation energy from the literature values. This is because the method used is Hartree-Fock instead of DFT so there is no proper basis for comparison. The use of different methods and basis sets will lead to different computational methods and accuracies, and all these small differences can sum up to a big difference in the final values.

==Conclusion==
In conclusion, the calculations above indicated that using the better basis set, such as 6-31G(d,p) instead of 3-21G will give more accurate results. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-15cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references />

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T18:10:32Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. In general, having an EDG will increase the energyl level while having an EWG will decrease the energy level. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T17:50:02Z

Qwt11: /* Conclusion */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==
The calculations made were complete and accurate as they converged. When frequency analysis was performed, steps were taken to ensure that all the low frequencies values were within the required range of +/-30cm-1. Comparisons between calculated results were made based on those produced from the same method and basis set in order to ensure accuracy.

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T17:40:42Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)]+ is found to be the least stable, followed by [N(CH3)3(CH2CN)]+ and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)]+ no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)]+ > [N(CH3)3(CH2CN)]+. The difference in energy gap can be observed experimentally by collection absorption spectrum of the cations as they will show peaks at different wavelength.

The energies of the HOMOs and LUMOs can affect the ability of the cations in interaction with other molecules. HOMOs are often seen as donor orbitals as they are the highest energy orbitals that contain electrons while LUMOs are often seen as acceptor orbitals as they are the most stable orbitals that do not contain any electrons. Hence the energy levels of the HOMOs and LUMOs can affect the nucleophilicity and electrophilicity of the ions. If we compare the energies of the 3 cations, the best donor orbital is the HOMO of [N(CH3)3(CH2OH)]+ as it is the least stable and will be the most reactive. In addition, the best acceptor orbital is the LUMO of [N(CH3)3(CH2CN)]+ as it is the most stable. However, whether the interaction is strong or weak is dependent on the energy levels of the HOMO or LUMO of the molecule the cation is interacting with. The best overlap comes when there is a small energy gap between the respective HOMO and LUMO involved in interaction.

==Conclusion==

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T17:25:53Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)] is found to be the least stable, followed by [N(CH3)3(CH2CN)] and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)] no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group. For the LUMOs, the stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)] . Once again, this is due to the balance of the amount of bonding interactions and anti-bonding interactions in the LUMOs.

The HOMO-LUMO gaps of the ions are affected by the change in energies caused by the influenced of the functional groups. The trend shows a decrease in the HOMO-LUMO gap [N(CH3)4]+ > [N(CH3)3(CH2OH)] > [N(CH3)3(CH2CN)].

==Conclusion==

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T17:21:00Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 
In the presence of the functional groups, the energies of the HOMO and LUMO has shifted. The HOMO of the [N(CH3)3(CH2OH)] is found to be the least stable, followed by [N(CH3)3(CH2CN)] and [N(CH3)4]+. This is due to a reduction of the bonding interactions and an increase in anti-bonding interactions in the HOMOs in the presence of the different functional groups. However, the comparison is weak, as the HOMO of [N(CH3)3(CH2CN)] no longer involves the methyl groups due to the electron-withdrawing effect of the -CN group.

For the LUMOs, the effect of the functional groups are more obvious. The stability of the LUMOs decrease from [N(CH3)3(CH2CN)] > [N(CH3)4]+ > [N(CH3)3(CH2OH)] .

==Conclusion==

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T17:14:32Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shape of HOMOs 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shape of LUMOs 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 

==Conclusion==

==References==
<references/>

Rep:Mod:qwt11 inorg ionicliquids

2013-11-21T17:14:03Z

Qwt11: /* HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

Mini Project - Ionic Liquids: Designer Solvents 
Qian Wen Tan 
CID: 00700342 
=Introduction=
Ionic liquids are ionic salts in the liquid state due to their low melting points. This is an anomaly from the usual ionic salts which have high melting points due to the high lattice energies caused by the strength of the ionic bonds. Hence, ionic liquids have their own special properties that can be engineered accordingly, leading to them being known as designer solvents. In this computational project, the properties of 3 'onium' ions and the influence of functional groups are explored.

=Comparison of selected 'onium' cations=
The selected 'onium' cations are [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+.
==[N(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26160}} 
Frequency Analysis:{{DOI|10042/26161}} 
Population Analysis:{{DOI|10042/26162}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
| style="text-align: center;" |-214.18126735 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00003015 a.u.
| style="text-align: center;" |0.00002996 a.u
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0002 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 9 minutes 24.3 seconds
| style="text-align: center;" |0 days 0 hours 9 minutes 6.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 12.7 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000667 0.001800 YES
RMS Displacement 0.000189 0.001200 YES
Predicted change in Energy=-6.645118D-08
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000071 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.258655D-07
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -19.4468 -12.6357 -0.0006 -0.0004 0.0009 5.1478
Low frequencies --- 178.8418 282.0168 285.4548
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for all calculations. In addition, all calculations also converged. The energy is calculated to be -214.18126735 a.u. for all. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. 
 

=== Selected Molecular Orbitals (MOs) ===
MO analysis were performed on 5 selected MOs of [N(CH3)4]+. These are MO #6, #10, #15, #17 and #21.
 
'''(I) MO 6: highly bonding'''
<center>[[File:NCH34_MO6A.png|500px|MO6]] 
'''Figure 1.1''': Molecular Orbital 6 - highly bonding </center>
Referring to Figure 1.1, MO 6 is a highly bonding MO where there are strong in-plane interactions between the s atomic orbitals of N and the C atoms (blue arrows), while the H atoms are not involved. In addition, there are also multiple moderately strong through space interactions between the orbitals(yellow arrows). There is no presence of any nodes as all the orbitals are in phase. Overall, this leads to a highly bonding MO. The MO is also highly delocalised with the orbitals overlapping such that the overall orbital covers nearly the whole molecule. The calculated energy is -1.19646a.u.. 
 
'''(I) MO 10: bonding'''
<center>[[File:NCH34_MO10A.png|500px|MO10]] 
'''Figure 1.2''': Molecular Orbital 10 - bonding </center>
Referring to Figure 1.2, MO 10 is a bonding orbital with 4 planar nodes (red circles). The nodes are the nodes in each p orbital of the C atoms. At each methyl group, the p orbital of C atom overlaps with the s orbital of the H atoms (nlue arrows). The orbitals formed have moderately strong through space in-phase interactions (yellow arrows). However, the through space in-phase interactions between methyl groups are weak. As a result the orbitals are localised at each methyl group. The opposite phase of the p orbitals of the C atoms also overlap with the s orbital of the N atom. As a result, there is strong out-of-phase interactions between the opposite phases. The central orbital is also quite localised on N. Overall the MO has more bonding interactions than anti-bonding interactions. The calculated energy is -0.80745 a.u..

 
'''(I) MO 15: non-bonding'''
<center>[[File:NCH34_MO15A.png|500px|MO15]] 
'''Figure 1.3''': Molecular Orbital 15 - non-bonding </center>
Referring to Figure 1.3, there are 4 planar nodes present at each C atom in MO 15. As a result, s orbitals of 2 H atoms of one methyl group will overlap with the p orbital of the C atom with in-phase interactions. This orbital will then form through space in-phase interactions with another similarly formed orbital at the methyl group beside it(yellow arrows). The remaining H atom will then form strong through space in-phase interaction with another H atom from another methyl group (yellow arrow), in addition to forming orbital overlap with the other phase of the p orbital of C atom. This pattern is consistent for all methyl groups present. Due to the presence of nodes, there is change of phase in the orbitals. Hence, strong through space out-of-phase interactions can be observed between H atoms in a single methyl group (pink arrows) and between orbitals with different phases in general. The N atom does not participate in this MO. The overall MO is non-bonding as the interactions are cancelled out by the anti-bonding interactions. The Mo is also delocalised as orbitals are formed from through space overlaps. The calculated energy is -0.62246a.u..

 
'''(I) MO 17: anti-bonding'''
<center>[[File:NCH34_MO17A.png|500px|MO17]] 
'''Figure 1.4''': Molecular Orbital 17 - anti-bonding </center>
Referring to Figure 1.4, MO 17 consists of 4 planar nodes at each C atom. 2 of the H atoms are not involved. Strong in-phase interaction can be seen between 2 H atoms in 2 of the methyl groups (yellow arrows), which also overlaps with p orbital of the C atom that has the same phase. The s orbital remaining H atom in the methyl group then overlaps in-phase with the other phase of the p orbital of the C atom. This occurs for all the methyl groups. The N atom is not involved in this MO. As the orbitals are of alternating phases, weak through space out-of-phase interactions (blue arrows) and strong out-of-phase interactions (pink arrows) can be observed, with the strength dependent on the distance between the orbitals. The change of phases are due to the presence of the planar nodes. In addition, there is also weak through space in-phase interactions between orbitals of the same phase (purple arrow). Overall, the MO is considered to be anti-bonding as there are many out-of-phase interactions. The MO is also largely delocalised due to the through space interactions. The calculated energy is -0.58034a.u..

 
'''(I) MO 21: highly anti-bonding'''
<center>[[File:NCH34_MO21A.png|500px|MO21]] 
'''Figure 1.5''': Molecular Orbital 21: highly anti-bonding </center>
Referring to Figure 1.5, MO 21 consists of 5 planar nodes at all the C atoms and the N atom. There are presence of strong in-phase overlap of the s orbitals of 2 H atoms in methyl group with the p orbital of the C atom. This occurs for all the methyl groups but 2 of the methyl groups have the same phase while the other 2 are of different phase. The remaining H atom then overlaps with the p orbital of the N atom and the other s orbital of the H atom on another methyl group. This also happens for the last 2 H atoms but with an opposite phase. As a result, there are multiple strong out-of-phase interactions(pink arrows). Hence, the overall MO is highly anti-bonding and delocalised. The calculated energy is -0.57933a.u..

==[P(CH3)4]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26163}} 
Frequency Analysis:{{DOI|10042/26164}} 
Population Analysis:{{DOI|10042/26165}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-500.82701295 a.u.
| style="text-align: center;" |-500.82701307 a.u.
| style="text-align: center;" |-500.82699130 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000467 a.u.
| style="text-align: center;" |0.00000445 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0001 Debye
| style="text-align: center;" |0.0002 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 22 minutes 5.2 seconds
| style="text-align: center;" |0 days 0 hours 20 minutes 25.0 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 53.5 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000003 0.000010 YES
Maximum Displacement 0.000051 0.000060 YES
RMS Displacement 0.000017 0.000040 YES
Predicted change in Energy=-1.415870D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-4.142589D-09
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.3301 -0.0012 0.0026 0.0032 2.1241 15.6018
Low frequencies --- 156.3266 191.6596 192.4282
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1 as tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that. In addition, the second set of frequencies have positive values, indicating minimum energies. However, upon close inspection of the energy levels, all of them are different for all 3 calculations although frequency analysis and population analysis were done using the optimised molecule from the optimisation using 6-31G(d,p). This occurred despite repeating the calculations. Having consulted the demonstrator, I was advised to leave the calculations as they are since the same file was used for further calculations. All 3 calculations have similar dipole moments. 
 

==[S(CH3)3]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26188}} 
Frequency Analysis:{{DOI|10042/26189}} 
Population Analysis:{{DOI|10042/26195}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68327532 a.u.
| style="text-align: center;" |-517.68326973 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000328 a.u.
| style="text-align: center;" |0.00000326 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
| style="text-align: center;" |0.9651 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 16.3 seconds
| style="text-align: center;" |0 days 0 hours 8 minutes 58.5 seconds
| style="text-align: center;" |0 days 0 hours 0 minutes 36.3 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000097 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.001015 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.682889D-07
Optimization completed.
-- Stationary point found.
</pre>

Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001786 0.001800 YES
RMS Displacement 0.000618 0.001200 YES
Predicted change in Energy=-1.159186D-08
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies
<pre>
Low frequencies --- -4.3477 -0.0008 -0.0008 0.0036 6.9781 9.4617
Low frequencies --- 161.8789 199.6201 200.6687
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. Tight convergence criteria was chosen and the keyword 'int=ultrafine scf(conver=9)' was used to ensure that the frequency analysis calculation converged. Once again, the problem of having different energies occurred despite repeating the calculations. As a result, the calculations were left as such as the optimised molecule was used for frequency analysis and population analysis. All 3 calculations have the same dipole moment of 0.9651D. 
 

==Comparisons between [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+==
=== Comparison of geometries ===
In the following table, X is given to be the heteroatom, which can either be N, P or S. 
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! X-C bond length/Å
| style="text-align: center;" |1.51
| style="text-align: center;" |1.82
| style="text-align: center;" |1.82
|-
! C-H bond length/Å
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
| style="text-align: center;" |1.09
|-
! H-C-H angle/o
| style="text-align: center;" |110.0
| style="text-align: center;" |109.0
| style="text-align: center;" |109.4/111.1
|-
! H-C-X angle/o
| style="text-align: center;" |108.9
| style="text-align: center;" |109.9
| style="text-align: center;" |107.3/110.6
|-
! C-X-C angle/o
| style="text-align: center;" |109.5
| style="text-align: center;" |109.5
| style="text-align: center;" |102.3
|-
|}
 
Bond lengths 
The calculated C-N bond length of 1.51Å is close to the reported value of 1.496(2)Å<ref name= "#1">J. F. Lehmann and G. J. Schrobilgen, Journal of the American Chemistry Society, 2005, 127, 9416–9427.</ref> in [N(CH3)4][BrO3F2]. The calculated C-P bond length of 1.82Å is also close to the reported value of 1.830(5)Å<ref name= "#2">G. Stringer, N. J. Taylor, and T. B. Marder, Acta Crystallographica , 1996, C52, 80–82.</ref> in [Co(CCH){P(CH3)3}4]. Finally, the calculated C-S bond length of 1.82Å is also in good agreement with the reported value of 1.837-1.839Å<ref name= "#3">H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko, J. R. Lewis, R. J. Mawhorter, H. E. Robertson, and D. W. H. Rankin, The Royal Society of Chemistry, 2005, 3221–3228.</ref> in Se(SCH3)2.

It can be observed that the C-N bond is significantly shorter than the C-P and the C-S bond. This is because N is in the second period of the Periodic Table of Elements, while P and S are in the third period, hence it is much less diffused with a larger effective nuclear charge. As a result, there is less electron-electron repulsion during bond formation. In addition, the orbital size is much similar to that of C, which is beside it in the Periodic Table of Elements, hence there will be better orbital overlap between N and C as compared to between P and C or S and C. Hence, a stronger bond will be formed, leading to a shorter C-X bond. The calculated P-C and S-C bond lengths are the same as P and S are just beside each other in the Periodic Table of Elements, hence they will have similar orbital overlap with C.
 

All the C-H bond lengths are identical, indicating that the heteroatom has no influence on it. 
Bond angles 
The angles about C-X-C for [N(CH3)4]+ and [P(CH3)4]+ are 109.5o, which ties in with the tetrahedral geometry. In the cations, N and P each loses 1 valence electron to be left with 4 valence electrons. All 4 electrons on N and P are used for bonding with the 4 methyl groups. Hence, the geometry about N and P is tetrahedral, which is clearly seen from the 109.5o. Sulfur belongs to group 16 on the Periodic Table of Elements. Hence, after removing 1 valence electron, there will be 5 left. Out of the 5 valence electrons, only 3 are used for bonding with 3 methyl groups, leading to a lone pair found on S. As a result, [S(CH3)3]+ has a trigonal pyramidal structure with an angle of 102.3o. The angle is smaller than that of [N(CH3)4]+ and [P(CH3)4]+ as the lone pair - bond pair repulsion is much greater. Hence the calculations have confirmed the structures of the 'onium' ions.

[S(CH3)3]+ is found to have 2 values each for the H-C-H bond angles and the H-C-S bond angles. This is due to the presence of the lone pair on S, which results in greater repulsion to the H atoms that are close to it. As a result the angle is reduced for the H-C-H and H-C-X angles for those H atoms close to S. 

=== NBO Charge Analysis ===

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[P(CH3)4]+
! style="text-align: center;" |[S(CH3)3]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO01.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO01.png|280px|MO21]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:P(CH3)4%2B_NBO02.png|280px|MO21]]
| style="text-align: center;" |[[File:S(CH3)3%2B_NBO02.png|280px|MO21]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |P: +1.667 C: -1.060 H: +0.298
| style="text-align: center;" |S: +0.917 C: -0.846 H: +0.297
|-
|}
<center>Table 1: Charge distribution of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 

The charge range is set to be -1.700 to +1.700 to allow proper comparison. Red indicates a negative charge and the lighter it is, the more negative the value. Similarly, green indicates positive charge, and the lighter it is, the more positive it is. Although all 3 cations are singly charged, they show different charge distribution as seen above.
 

The charges of the heteroatoms N, P and S tie in with their electronegativity where N > S> P. Hence, P is seen to have the highest positive charge of +1.667 while N is seen to be negatively charge with a value of -0.295. Comparing the charges on the C atoms in all 3 cations, it can be observed that they show great differences, with the C atom in [N(CH3)4]+ being the least negative (-0.483) while the C atom in [P(CH3)4]+ being the most negative (-1.060). This is in line with the previous argument, the C atom that is attached to the more negatively charge heteroatom will be relatively more positive. The H atoms for [P(CH3)4]+ and [S(CH3)3]+ have similar charge values. However, the H atoms in [N(CH3)4]+ are slightly less positive. This is due to the less negatively charged C atoms. Overall, all 3 cations have their charges summed up to 1, which is expected. However, although N is usually drawn to hold the formal +1 charge in the cation, it can be observed that it is still negatively charged due to its electronegativity.
 
 

=== NBO Population Analysis ===

{| class="wikitable"
! style="text-align: center;" |Molecules
! style="text-align: center;" |Relative contributions/ %
! style="text-align: center;" |Electronegativities<ref name= "#4">P. Atkins, T. Overton, J. Rourke, M. Weller, and F. Armstrong, Inorganic Chemistry, Oxford University Press, Oxford, 5th edn., 2010.</ref>
! style="text-align: center;" |Difference in electronegativities (X-C)
|-
! [N(CH3)4]+
| style="text-align: center;" | <pre>( 33.65%) 0.5801* C 1 s( 20.78%)p 3.80( 79.06%)d 0.01( 0.16%)</pre><pre>( 66.35%) 0.8145* N 17 s( 25.00%)p 3.00( 74.96%)d 0.00( 0.03%)</pre>
| style="text-align: center;" |C: 2.55 N: 3.04
| style="text-align: center;" |0.49
|-
! [P(CH3)4]+
| style="text-align: center;" |<pre>( 59.57%) 0.7718* C 1 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)</pre><pre>( 40.43%) 0.6358* P 17 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)</pre>
| style="text-align: center;" |C: 2.55 P: 2.19
| style="text-align: center;" |0.36
|-
! [S(CH3)3]+
| style="text-align: center;" |<pre>( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)</pre><pre>( 51.33%) 0.7164* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)</pre>
| style="text-align: center;" |C: 2.55 S: 2.58
| style="text-align: center;" |0.03
|-
|}
<center>Table 2: NBO population analysis of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)3]+</center> 
The NBO population analysis data above shows the % contribution of the C atom and the X atom (N/P/S) to the C-X bond. In general, the orbitals at C and X are all sp3 hybridised orbitals although the contribution from the s orbital and the p orbital slightly deviates for the C atoms in [N(CH3)4]+ and [S(CH3)3]+. It is also noted that the S atom has the largest deviation as it has more diffused orbitals so the hybridisation deviates from sp3. When looking at their relative contributions, the trend shows a decreasing contribution from the X atom where N >S > P. In particular, C contributes more to the C-X bond than P in [P(CH3)4]+.

This can be explained by looking at the respective electronegativities of the atoms and the difference in electronegativities between C and X. In general, all the C-X bonds are covalent with varying degree of ionic character according to the magnitude of the differences in electronegativities. The electronegativity difference in the C-X bond decreases from C-N > C-P > C-S. In a bond, the more electronegative atom is expected to have a larger relative contribution as it has a high tendency to draw the electron pair to itself. This is observed above, in each C-X bond, the more electronegative atom (N for [N(CH3)4]+, C for [P(CH3)4]+ and S for [S(CH3)3]+) shows a greater contribution. In addition, the relative contribution is related to the difference in electronegativity between C and X. For [N(CH3)4]+, the electronegativity difference (0.49) is the greatest, hence N contributes significantly more than C to the C-N bond. On the other hand, the electronegativity difference between C and S in [S(CH3)3]+ is very small, such that each of them contributes about the same % to the C-X bond, with S contributing slightly more as it is slightly more electronegative than C.

With such an observation, it will be expected that the electronegativity difference indicates that N should hold large negative charge while C should hold large positive charge in the C-N bond. Yet this is not observed in the charge distribution. In fact, the charge distribution shows a negative charge for N and an even more negative charge for C. This is because the N atom no longer has the usual 5 valence electrons, but instead, has only 4 valence electrons as a cation is formed. As a result, this will reduce the electronegativity of the N atom, hence decreasing its negative charge. In addition, the overall positive charge is delocalised throughout the cation and not localised on the N atom, hence the negative charge on N is maintained.

Further explanation is derived from the fact that C and N are beside each other in the Periodic Table of Elements. As a result, the orbital overlap in the formation of the C-N bond is large. This can lead to a contribution of the electronegativity on N to the C atom, which can then lead to a more negative charge than usual. More importantly, the C atoms are surrounded by electropositive H atoms. Given that the overall charge is +1, the overall charge distribution has to be distributed such that the sum of all the charges = 1 while at the same time, maintaining the negative charge on the electronegative N and the positive charge on the electropositive H atoms. As a result, this lead to negative charges on C atoms, despite them being more electropositive than N, which is unexpected. In this case, C-N bond has the highest ionic character out of all the C-X bonds due to the greatest electronegativity difference.

For the C-P bond, it can be seen that P is more electropositive than C. This also ties in with the charge distribution seen above, where P has a charge of +1.667 and C has a charge of -1.060. In this case, it is expected for C to have a negative charge as it is more electronegative relative to P. Furthermore, with the formation of a cation, the P atom has 1 less valence electron, leading to a greater positive charge. Since P is electropositive, the +1 charge will be localised on it. Furthermore, the C atoms are now surrounded by electropositive P atom and H atoms. Hence, they will be highly negatively charged. Overall, this corresponds to the % contribution where P contributes less as it is more electropositive. Once again, the C-P bond has ionic character as the electronegativity difference is 0.36.

For the C-S bond, there is very small electronegativity difference between C and S (0.03). Hence, the C-S bond can be considered non-polar and is highly covalent. This means that there is nearly equal % contribution from each atom to the C-S bond, which is observed. Although S is slightly more electronegative than C, it has a charge of +0.917 while C has a charge of -0.846. This contradictory data indicates that the overall +1 charge of the cation is localised on S.
 

=== Formal charge in [NR4]+===
Traditionally, the 'formal' positive charge on N is shown to be localised on N in [N(CH3)4]+. This is because there is one valence electron removed from N to give only 4 valence electrons which will bond with the methyl groups. However, as seen previously, the N atom in [N(CH3)4]+ has a charge value of -0.295, implying that it is incorrect to draw the positive charge on N. Instead, this positive charge is delocalised to all the H atoms in [N(CH3)4]+ as they are the most electropositive atoms in the molecule.

=Influence of functional groups=
In order to observe the influence of functional groups on the ionic liquids, data were calculated for [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+.

==[N(CH3)3(CH2OH)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26270}} 
Frequency Analysis:{{DOI|10042/26271}} 
Population Analysis:{{DOI|10042/26272}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39470724 a.u.
| style="text-align: center;" |-289.39471219 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000048 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1357 Debye
| style="text-align: center;" |2.1356 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 29 minutes 13.0 seconds
| style="text-align: center;" |0 days 0 hours 24 minutes 6.7 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 1.4 seconds
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000015 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-7.863587D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-1.186848D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -8.4541 -5.0324 -1.1157 -0.0009 -0.0009 -0.0008
Low frequencies --- 131.1059 213.4594 255.7116
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-15cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. It can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==[N(CH3)3(CH2CN)]+==
=== Data ===
DOIs 
Optimisation: {{DOI|10042/26210}} 
Frequency Analysis:{{DOI|10042/26211}} 
Population Analysis:{{DOI|10042/26212}} 
 
Summary of results 
{| class="wikitable"
! Calculation
! style="text-align: center;" |Optimisation using 6-31G(d,p)
! style="text-align: center;" |Frequency Analysis
! style="text-align: center;" |Population Analysis
|-
! File Type
| style="text-align: center;" |.log
| style="text-align: center;" |.log
| style="text-align: center;" |.log
|-
! Calculation Type
| style="text-align: center;" |FOPT
| style="text-align: center;" |FREQ
| style="text-align: center;" |SP
|-
! Calculation Method
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
| style="text-align: center;" |RB3LYP
|-
! Basis Set
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
| style="text-align: center;" |6-31G(d,p)
|-
! Charge
| style="text-align: center;" |1
| style="text-align: center;" |1
| style="text-align: center;" |1
|-
! Spin
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
| style="text-align: center;" |Singlet
|-
! E(RB3LYP)
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39376383 a.u.
| style="text-align: center;" |-306.39377031 a.u.
|-
! RMS Gradient Norm
| style="text-align: center;" |0.00000040 a.u.
| style="text-align: center;" |0.00000053 a.u.
| style="text-align: center;" |-
|-
! Dipole Moment
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7642 Debye
| style="text-align: center;" |5.7640 Debye
|-
! Point Group
| style="text-align: center;" |C1
| style="text-align: center;" |C1
| style="text-align: center;" |C1
|-
! Job cpu time
| style="text-align: center;" |0 days 0 hours 23 minutes 35.6 seconds
| style="text-align: center;" |0 days 0 hours 26 minutes 37.3 seconds
| style="text-align: center;" |0 days 0 hours 1 minutes 21.4 seconds.
|}
 
Final sets of forces and displacements for optimisation using 6-31G(d,p)
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000040 0.000060 YES
RMS Displacement 0.000007 0.000040 YES
Predicted change in Energy=-9.002465D-12
Optimization completed.
-- Stationary point found.
</pre>
 
Final sets of forces and displacements for frequency analysis
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000074 0.001800 YES
RMS Displacement 0.000020 0.001200 YES
Predicted change in Energy=-3.467927D-11
Optimization completed.
-- Stationary point found.
</pre>
 
Low frequencies
<pre>
Low frequencies --- -2.5807 -0.0009 -0.0007 -0.0004 7.1537 9.6772
Low frequencies --- 91.7766 154.0307 210.9339
</pre>
 
Optimisation was performed using the basis set 6-31G(d,p). The RMS gradient norm is <0.001 and close to 0 for both. In addition, all calculations also converged. The 6 low frequencies (first line) are also within the required range of +/-30cm-1. In addition, the second set of frequencies have positive values, indicating minimum energies. All 3 calculations have similar dipole moments. Once again, it can be observed that the energy from the population analysis is slightly different from that of the optimisation and frequency analysis. However, as previously advised, the calculation was left alone since the optmised molecule was used for population analysis. 
 

==Comparison of charge distribution on [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==

{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! Charge by colour
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO03.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO01.png|280px|NBO01]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO01.png|280px|NBO01]]
|-
! Labelled charges
| style="text-align: center;" |[[File:N(CH3)4%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_NBO02.png|280px|NBO02]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_NBO02.png|280px|NBO02]]
|-
! Charge values
| style="text-align: center;" |N: -0.295 C: -0.483 H: +0.269
| style="text-align: center;" |N: -0.322 C: -0.494(CH3)/ -0.492(CH3)/ -0.491(CH3)/ +0.088(CH2OH) H: +0.262-0.282(CH3)/ +0.249(CH2)/ +0.237CH2)/ +0.521(-OH) O: -0.725
| style="text-align: center;" |N: -0.289/ -0.186(CN) C: -0.489(CH3)/ -0.485(CH3)/ -0.358(CH2CN)/ +0.209 (CN) H: +0.269-0.282(CH3)/ +0.309(CH2)
|-
|}
<center>Table 3: Charge distribution of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 
The charge range has been set to -0.725 to 0.725 for proper comparison. Red represents negative charge where the more negative it is, the lighter the red colour. Similarly, green represent positive charge where the more positive it is, the lighter the green colour. The effect on the charge distribution with a change in functional groups can be seen by observing the difference in charge distributions when comparing [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+. -OH is an electron donating group (EDG) while -CN is an electron withdrawing group (EWG).
 

At first glance, by replacing one H atom on -CH3 to -OH, the charge on the central N atom became more negatively charged while doing so with -CN lead a less negatively charge N atom. This is because -OH is an EDG that can donate electron density to the central N atom due to the lone pairs on O. Similarly, -CN draws the electron density away from the central N atom, hence making it less negative.
 

It can also be observed that the C atoms on the non-substituted methyl groups are not significantly affected by the change in functional group, with their charge values only slightly more negative (ranging from -0.485 to -0.494 than that found in [N(CH3)4]+ (-0.483). In addition, the C atoms now have varying charge values as the overall structure is no longer symmetrical with a proper tetrahedral structure. Hence the charge distribution will vary a little. This is confirmed by looking at the N-C bond lengths where the N-COH (1.53Å) and N-CN (1.55Å) bonds are both longer than the N-CH3 (1.50-1.51Å).

The effect of -OH as an EDG can be observed by looking at the charge value of the C atom attached to it. Unlike the other C atoms, this particular C atom has a positive charge value of 0.088. This seems unexpected as -OH is expected to donate more electron density and the C atom should have an even more negative charge value. However, O is a highly electronegative atom and will be expected to withdraw electron density from its surrounding atoms. As a result, it has a charge value of -0.725. In additional, this causes the hydroxyl H atom to be highly electropositive (+0.521) when compared to the H atoms found on the methyl groups (+0.269 to +0.282). The H atoms of the methyl groups have similar charge values to those found in [N(CH3)4]+. The H atoms in -CH2OH are found to be slightly less electropositive than usual. This indicates that they are also affected by the electron-donating ability of the -OH group, which donates electron density through the C-N frame work.
 

When looking at [N(CH3)3(CH2CN)]+, it can once again be observed that the C atoms of the methyl groups are not significantly affected by the electron-withdrawing effect of the -CN group, as their charge values range from -0.485 to -0.489. This also applies for the H atoms in the methyl group which have similar charge values to those found in [N(CH3)4]+. However, it can be seen that the C atom next to the -CN group has its electron density withdrawn as it now has a less negative charge value of -0.358 when compared to the rest. In the -CN functional group, it can be observed that the electronegative N atom is withdrawing electron density as the charge on the C atom is positive with a value of 0.209. This is a significant difference from the C atoms in the methyl groups which are also attached to a N atom. This is because the CN is triply bonded. Similarly, due to the electron-withdrawing effect of the -CN group, the H atoms in -CH2CN are found to be slightly more electropositive than usual.
 

Overall, the charges all sum up to 1 for all the ions.
 

==HOMO and LUMO of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+==
{| class="wikitable"
! Molecules
! style="text-align: center;" |[N(CH3)4]+
! style="text-align: center;" |[N(CH3)3(CH2OH)]+
! style="text-align: center;" |[N(CH3)3(CH2CN)]+
|-
! HOMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_HOMO01.png|280px|HOMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_HOMO01.png|280px|HOMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.57933
| style="text-align: center;" |-0.48763
| style="text-align: center;" |-0.50048
|-
! LUMOs
| style="text-align: center;" |[[File:N(CH3)4%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2OH)%2B_LUMO01.png|280px|LUMO]]
| style="text-align: center;" |[[File:N(CH3)3(CH2CN)%2B_LUMO01.png|280px|LUMO]]
|-
! Energies of HOMO/ a.u.
| style="text-align: center;" |-0.13302
| style="text-align: center;" |-0.12459
| style="text-align: center;" |-0.18183
|-
! Energy differences/ a.u.
| style="text-align: center;" |0.44631
| style="text-align: center;" |0.36304
| style="text-align: center;" |0.31865
|-
|}
<center>Table 4: HOMOs and LUMOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+</center> 

Shapes of HOMO 
In the HOMO of [N(CH3)4]+, 2 H atoms in 2 methyl groups (Atoms #6, #8, #11, #12) are not involved, while 1 H atom in each of the remaining methyl groups are also not involved (Atoms #4 and #16). There are a total of 5 planar nodes, found at the C atoms and the N atom. For the methyl groups with only 1 H atom involved, the p orbital of the C atom overlaps in phase with the s atomic orbital of the H atom while the other phase overlaps in phase with the p orbital of the N atom. For the methyl groups with 2 H atoms involved, 1 H atom overlaps in phase with the p orbital of the C atom while the other H atom overlaps in phase with the opposite phase of the same p orbital. There is strong through space in phase interactions between the same phase orbitals formed from the overlap mentioned above.

In the HOMO of [N(CH3)3(CH2OH)]+,less atoms (Atoms H#5, H#6, H#7, H#9, H#11, H#13, H#14 not involved) are involved and the orbitals are concentrated at the -OH region. In 2 of the methyl groups, only 1 H atom is involved, and the s orbitals overlap in-phase with the p orbitals of the C atoms. The other phase of all 3 p orbitals of the C atoms in the methyl groups then overlap in phase with the p orbital of the N atom. The other phase of the p orbital overlaps in phase with the p orbital of the C atom beside the -OH group. The remaining phase of this C orbital overlaps with one of the H atoms it is attached to. The lone pair in the p orbital of the O in -OH is also involved in the HOMO. Overall there is a change in the shape of the HOMO in the presence of the -OH group as it is no longer symmetrical in shape. The donation of electron density to N atom from the -OH has resulted in larger orbital seen. Also, the p orbital of O that contains the lone pair show is large, such that it surrounds the hydroxyl H atom without interacting with it, hence indicative of the large amount of electron density at -OH.

In the HOMO of [N(CH3)3(CH2CN)]+, even less atoms are now involved. The HOMO is highly concentrated on the C-CN fragment of the ion. The p orbitals of C and N on -CN overlap in phase and there out-of-phase interaction with the p orbital on N. This results in a greater change in shape of the HOMO as it is now localised at CN. Due to the electron-withdrawing effect of the -CN group, the HOMO does not involve the methyl groups. 
 

Shapes of LUMO 
In the LUMO of [N(CH3)4]+, the p orbitals of the C atoms in the methyl group overlap in phase for one of the phase. This overlap is strong and large as the orbital formed is highly delocalised. In the core of the ion lies the s orbital of the N, which is of opposite phase to the large orbital formed by the p orbitals of the C atoms and there is strong out-of-phase interaction between the 2. Similarly, there is also strong out of phase interaction with the opposite phases of the p orbitals on C. Overall the shape of the LUMO is symmetrical.

In the LUMO of [N(CH3)3(CH2OH)]+, similar interactions are seen in the methyl groups with the N atom. However, there is now in-phase overlap of the s orbital of the N atom with the s orbital of the C atom that is right next to the -OH group. This overlap also involves the sp3 orbital containing the lone pair in O. The H atoms of the CH2 OH fragment are also involved in in-phase overlap with the methyl groups. The shape of the LUMO is no longer symmetrical, because of the different types of orbital overlaps involved with the -OH group.

In the LUMO of [N(CH3)3(CH2CN)]+, the p orbital of the C atom beside the -CN group now overlaps in phase with the p orbital of the C atom in the -CN group. This orbital has out of phase interactions (anti-bonding) with the p orbital of the N atom in the -CN group. In addition, due to the electron withdrawing effect of the -CN group, the H atoms of the methyl groups are no longer involved in the LUMO has their electron density has been withdrawn. This reduces the size of the orbital formed from the favourable overlap of the p orbitals of the C atoms in the methyl groups. As a result, the shape of the LUMO is also no longer symmetrical. 
 

Energies of HOMOs and LUMOs 

==Conclusion==

==References==
<references/>